Ahora Opciones Binarias general pico en español: Ma 1 Media Móvil

2.1 Modelos de media móvil (modelos MA)

Modelos de series temporales conocidos como modelos ARIMA pueden incluir términos autorregresivos y / o términos de media móvil. En la semana 1, aprendimos un término autorregresivo en un modelo de series de tiempo para la variable x t es un valor retrasado de x t. Por ejemplo, un término autorregresivo de retardo 1 es x t-1 (multiplicado por un coeficiente). Esta lección define los términos del promedio móvil.

Un término medio móvil en un modelo de serie temporal es un error pasado (multiplicado por un coeficiente).

Dejamos que \ (w_t \ overset N (0, \ sigma ^ 2_w) \), lo que significa que los w t son idéntica, independientemente distribuidos, cada uno con una distribución normal con media 0 y la misma varianza.

El modelo de media móvil de primer orden, denotado por MA (1) es

\ (X_t = \ mu + w_t + \ theta_1w_ \)

El modelo de media móvil de orden 2, denotado por MA (2) es

\ (X_t = \ mu + w_t + \ theta_1w_ + \ theta_2w_ \)

El modelo de media móvil de orden q, denotado por MA (q) es

\ (X_t = \ mu + w_t + \ theta_1w_ + \ theta_2w_ + \ dots + \ theta_qw_ \)

Nota . Muchos libros de texto y programas de software definen el modelo con signos negativos antes de los términos θ. Esto no cambia las propiedades teóricas generales del modelo, si bien cambia los signos algebraicos de los valores estimados de los coeficientes y los términos (no cuadrados) θ en las fórmulas para ACF y las varianzas. Usted necesita comprobar su software para verificar si los signos negativos o positivos se han utilizado con el fin de escribir correctamente el modelo estimado. R utiliza signos positivos en su modelo subyacente, como lo hacemos aquí.

Propiedades teóricas de una serie temporal con un modelo MA (1)

Obsérvese que el único valor distinto de cero en el ACF teórico es para el retardo 1. Todas las demás autocorrelaciones son 0. Por lo tanto, una ACF de muestra con una autocorrelación significativa sólo con el retardo 1 es un indicador de un posible modelo MA (1).

Para los estudiantes interesados, las pruebas de estas propiedades son un apéndice a este folleto.

Ejemplo 1 Supongamos que un modelo MA (1) es x t = 10 + w t + .7 w t-1. Donde \ (w_t \ overset N (0,1) \). Así, el coeficiente θ 1 = 0,7. El ACF teórico está dado por

Una trama de este ACF sigue.

La gráfica que se muestra es la ACF teórica para un MA (1) con θ 1 = 0,7. En la práctica, una muestra no suele proporcionar un patrón tan claro. Usando R, simulamos n = 100 valores de muestra usando el modelo x t = 10 + w t + .7 w t-1 donde w t

Iid N (0,1). Para esta simulación, sigue un diagrama de series de tiempo de los datos de la muestra. No podemos decir mucho de esta trama.

A continuación se muestra el ACF de muestra para los datos simulados. Observamos que el ACF de la muestra no coincide con el patrón teórico de la MA subyacente (1), que es que todas las autocorrelaciones para los retrasos de 1 serán Ser 0. Una muestra diferente tendría una ACF de muestra ligeramente diferente mostrada abajo, pero probablemente tendría las mismas características amplias.

Propiedades Terapéuticas de una Serie de Tiempo con un Modelo MA (2)

Para el modelo MA (2), las propiedades teóricas son las siguientes:

Obsérvese que los únicos valores distintos de cero en el ACF teórico son para los retornos 1 y 2. Las autocorrelaciones para retardos mayores son 0. Por lo tanto, una ACF de muestra con autocorrelaciones significativas en los retornos 1 y 2, pero autocorrelaciones no significativas para retardos más altos indica una posible MA (2) modelo.

Iid N (0,1). Los coeficientes son θ 1 = 0,5 y θ 2 = 0,3. Como se trata de un MA (2), el ACF teórico tendrá valores distintos de cero sólo en los retornos 1 y 2.

Los valores de las dos autocorrelaciones no nulas son

A continuación se muestra una gráfica del ACF teórico.

Como casi siempre es el caso, los datos de la muestra no se comportarán tan perfectamente como la teoría. Se simularon n = 150 valores de muestra para el modelo x t = 10 + w t + .5 w t-1 + .3 w t-2. Donde wt

Iid N (0,1). A continuación se muestra el gráfico de la serie de tiempo de los datos. Al igual que con el gráfico de la serie de tiempo para los datos de la muestra MA (1), no se puede decir mucho de ella.

A continuación se muestra el ACF de muestra para los datos simulados. El patrón es típico para situaciones donde un modelo MA (2) puede ser útil. Hay dos "picos" estadísticamente significativos en los intervalos 1 y 2, seguidos por valores no significativos para otros retrasos. Tenga en cuenta que debido al error de muestreo, la muestra ACF no coincide exactamente con el patrón teórico.

ACF para Modelos Generales MA (q)

Una propiedad de los modelos MA (q) en general es que hay autocorrelaciones no nulas para los primeros q retrasos y autocorrelaciones = 0 para todos los retrasos & gt; Q.

No unicidad de la conexión entre los valores de θ 1 y \ (\ rho_1 \) en el modelo MA (1).

En el modelo MA (1), para cualquier valor de θ 1. El 1 / θ 1 recíproco da el mismo valor para

Como ejemplo, utilice +0.5 para θ 1. Y luego utilice 1 / (0.5) = 2 para θ 1. Obtendrá \ (\ rho_1 \) = 0.4 en ambas instancias.

Para satisfacer una restricción teórica llamada invertibilidad. Se restringe los modelos MA (1) para tener valores con valor absoluto menor que 1. En el ejemplo dado, θ 1 = 0.5 será un valor de parámetro permisible, mientras que θ 1 = 1 / 0.5 = 2 no.

Invertibilidad de los modelos MA

Se dice que un modelo de MA es invertible si es algebraicamente equivalente a un modelo de AR de orden infinito convergente. Al converger, queremos decir que los coeficientes de AR disminuyen a 0 a medida que retrocedemos en el tiempo.

Invertibilidad es una restricción programada en el software de series de tiempo utilizado para estimar los coeficientes de los modelos con términos MA. No es algo que buscamos en el análisis de datos. En el apéndice se proporciona información adicional sobre la restricción de la invertibilidad para los modelos MA (1).

Nota de Teoría Avanzada. Para un modelo MA (q) con un ACF especificado, sólo hay un modelo invertible. La condición necesaria para la invertibilidad es que los coeficientes θ tienen valores tales que la ecuación 1-θ 1 y-. - θ q y q = 0 tiene soluciones para y que caen fuera del círculo unitario.

Código R para los Ejemplos

En el Ejemplo 1, se representó la ACF teórica del modelo x t = 10 + w t +. 7w t - 1. Y luego se simularon n = 150 valores de este modelo y se representaron las series de tiempo de muestra y la muestra ACF para los datos simulados. Los comandos R utilizados para trazar el ACF teórico fueron:

Acfma1 = ARMAacf (ma = c (0.7), lag. max = 10) # 10 retrasos de ACF para MA (1) con theta1 = 0.7 lags = 0: 10 #crea una variable llamada lags que va de 0 a 10. plot (A) (a = 0) #adds a (a) (a = 1) = a, Eje horizontal de la parcela

El primer comando determina el ACF y lo almacena en un objeto llamado acfma1 (nuestra elección de nombre).

El comando plot (el tercer comando) representa un retraso con respecto a los valores ACF para los retornos 1 a 10. El parámetro ylab etiqueta el eje y y el parámetro "main" pone un título en la gráfica.

Para ver los valores numéricos de la ACF simplemente utilice el comando acfma1.

La simulación y las parcelas se realizaron con los siguientes comandos.

Xc = arima. sim (n = 150, lista (ma = c (0.7))) #Simula n = 150 valores de MA (1) x = xc + 10 # agrega 10 para hacer media = 10. Simulación por defecto = (X, tipo = "b", principal = "Datos simulados de MA (1)") acf (x, xlim = c (1,10), principal = "ACF para datos de muestra simulados"

En el Ejemplo 2, se representó gráficamente la ACF teórica del modelo x t = 10 + w t + .5 w t-1 + .3 w t-2. Y luego se simularon n = 150 valores de este modelo y se representaron las series de tiempo de muestra y la muestra ACF para los datos simulados. Los comandos R utilizados fueron

Acfma2 = ARMAacf (ma = c (0.5.0.3), lag. max = 10) acfma2 lags = 0: 10 trama (retrasos, acfma2, xlim = c (1,10), ylab = "r", type = "h (= 0, x = 0) xc = arima. sim (n = 150, lista (ma = c (0,5, 0,3))) x = Xc + 10 gráfico (x, tipo = "b", principal = "serie MA simulada") acf (x, xlim = c (1,10), principal = )

Apéndice: Prueba de Propiedades de MA (1)

Para los estudiantes interesados, aquí hay pruebas de las propiedades teóricas del modelo MA (1).

Variable: \ (\ text (x_t) = \ text (\ mu + w_t + \ theta_1 w_) = 0 + \ text (w_t) + \ text (\ theta_1w_) = \ sigma ^ 2_w + \ theta ^ 2_1 \ sigma ^ 2_w = (1+ \ theta ^ 2_1) \ sigma ^ 2_w \)

Cuando h = 1, la expresión anterior = θ 1 σ w 2. Para cualquier h ≥ 2, la expresión anterior = 0. La razón es que, por definición de independencia del w t. E (w k w j) = 0 para cualquier k ≠ j. Además, debido a que w t tiene una media 0, E (w j w j) = E (w j 2) = σ w 2.

Para una serie de tiempo,

Aplique este resultado para obtener el ACF dado anteriormente.

Un modelo inversible MA es uno que puede ser escrito como un modelo de orden infinito AR que converge para que los coeficientes AR convergen a 0 a medida que avanzamos infinitamente en el tiempo. Vamos a demostrar la invertibilidad para el modelo MA (1).

Entonces sustituimos la relación (2) por wt-1 en la ecuación (1)

(3) \ (z_t = w_t + \ theta_1 (z_ - \ theta_1w_) = w_t + \ theta_1z_ - \ theta ^ 2w_ \)

En el instante t-2. La ecuación (2) se convierte en

Entonces sustituimos la relación (4) para wt-2 en la ecuación (3)

\ (Z_t = w_t + \ theta_1 z_ - \ theta_2_1w_ = w_t + \ theta_1z_ - \ theta_2_1 (z_ - \ theta_1w_) = w_t + \ theta_1z_ - \ theta_1 ^ 2z_ + \ theta ^ 3_1w_ \)

Si continuáramos (infinitamente), obtendríamos el modelo de orden infinito AR

\ (Z_t = w_t + \ theta_1 z_ - \ theta ^ 2_1z_ + \ theta ^ 3_1z_ - \ theta ^ 4_1z_ + \ dots \)

Obsérvese, sin embargo, que si | θ 1 | ≥1, los coeficientes multiplicando los retardos de z aumentarán (infinitamente) en tamaño a medida que retrocedamos en el tiempo. Para evitar esto, necesitamos | θ 1 | & Lt; 1. Esta es la condición para un modelo de MA (1) invertible.

Modelo Infinite Order MA

En la semana 3, veremos que un modelo AR (1) se puede convertir en un modelo de orden infinito MA:

\ (X_t - \ mu = w_t + \ phi_1w_ + \ phi ^ 2_1w_ + \ dots + \ phi ^ k_1 w_ + \ dots = \ sum_ ^ \ phi ^ j_1w_ \)

Esta suma de términos de ruido blanco pasado se conoce como la representación causal de un AR (1). En otras palabras, x t es un tipo especial de MA con un número infinito de términos remontándose en el tiempo. Esto se denomina un orden infinito MA o MA (∞). Una orden finita MA es un orden infinito AR y cualquier orden finito AR es un orden infinito MA.

Recordemos en la semana 1, observamos que un requisito para un AR estacionario (1) es que | φ 1 | & Lt; 1. Vamos a calcular el Var (x t) utilizando la representación causal.

Este último paso usa un hecho básico acerca de series geométricas que requiere \ (| \ phi_1 | & lt; 1 \); De lo contrario la serie diverge.

Navegación

Promedios móviles (MA)

El promedio móvil, o promedio móvil simple, representa la media de los últimos precios de cierre varios. El promedio móvil es simple de calcular, fácil de entender y confiable en pruebas. Esta simplicidad es la fuerza de la media móvil.

El promedio móvil básico se calcula igual que cualquier otro promedio matemático. La manera más común de determinar la media móvil de un mercado es tomar el precio de cierre durante un cierto número de días, agregarlos juntos y dividir por el número de días seleccionados.

Se suele pensar que los promedios móviles son indicadores de tendencia. Por ejemplo, la interpretación convencional es que una vez que los precios pasan de debajo de la media móvil por encima de ella, la tendencia se considera hacia arriba. Por otro lado, si los precios van desde arriba de la media móvil por debajo de ella, la tendencia del mercado se considera hacia abajo.

El propósito de la media móvil simple es seguir el progreso de la tendencia. Los promedios móviles pueden mantenerlo en la tendencia durante mucho tiempo. La media móvil le da una indicación de la tendencia hacia arriba (precios por encima de la media móvil) o hacia abajo (por debajo de la media móvil). Sin embargo, la media móvil no da ninguna indicación de la duración o duración de la tendencia.

Media móvil doble

Los promedios móviles dobles usan dos promedios diferentes en tándem. El primer promedio es generalmente un promedio que reacciona más rápidamente usando un período más corto de tiempo, generalmente 10 días. El segundo promedio es un promedio de reacción más lento que indicará un movimiento de precios a más largo plazo.

El uso de estos dos promedios en conjunto ayuda a aliviar los whipsaws dando una base de comparación. El promedio más rápido que rompe por encima del promedio más lento es una señal de compra, el promedio más rápido rompiendo por debajo del promedio más lento es una señal de venta.

Cuando se utilizan dos medias móviles diferentes, el comerciante obtiene una imagen más clara de las indicaciones de precios. Al combinar un promedio más lento de 20 días, con un promedio de 10 días más rápido, usted puede ver donde van las indicaciones a largo plazo.

Usted vendería una vez que el promedio móvil más rápido cruza debajo de la tendencia más lenta porque eso es una indicación del cambio en tendencia. Los precios a corto plazo deberían aumentar a un ritmo mayor que los precios a largo plazo en un buen mercado de tendencias al alza, y viceversa para una tendencia a la baja.

Promedio móvil triple

El sistema de promedios móviles triples se emplea trazando tres promedios móviles diferentes juntos. El primero de estos promedios es un promedio más rápido que sólo mira a la dirección de precios a corto plazo. El segundo promedio es un promedio medio que reacciona a un período de tiempo más largo, pero no tanto como el promedio final. El tercer promedio es el más lento para reaccionar, ya que toma un promedio del período más largo de tiempo.

Un sistema de media móvil de 10, 20 y 40 días se consideraría un promedio móvil triple. El primer promedio, el de 10 días, es el más rápido para moverse cuando los precios muestran un cambio. El segundo promedio, el de 20 días, es el promedio medio que no muestra cambios hasta que los precios se han movido por un período de tiempo más largo. Finalmente, el movimiento más lento de los promedios es el de 40 días. Este promedio lento no indicará una diferencia hasta que los precios hayan hecho un movimiento significativo. Las medias móviles a más corto plazo, al ser más sensibles a los cambios en el precio, se dice que siguen la tendencia más de cerca. El promedio medio o medio seguiría menos de cerca y el promedio más lento o menos sensible sería el más rezagado.

El uso de la media móvil triple es comprar cuando los tres promedios se mueven para estar en una tendencia al alza o para vender cuando estos promedios están en una tendencia bajista. La tendencia al alza aparece cuando el promedio más rápido es más alto que el de los otros promedios, el medio está por encima del más lento y el promedio móvil a más largo plazo está en el fondo.

Esta mirada sería invertida para una tendencia bajista fuerte con el promedio lento en la tapa, seguido por el promedio medio, y el más rápido en la parte inferior.

Cálculo

Mat: El promedio móvil para el período actual. Pn: El precio para el n-ésimo intervalo. N: La longitud de la media móvil.

Calcule el promedio de los últimos n intervalos utilizando el precio especificado para ese período. Ahora use valores reales para calcular un promedio móvil de cinco intervalos. Si usted asume los siguientes precios, los cálculos están aquí:

MA = (7380 + 7375 + 7385 + 7390 + 7395) / 5 = 36925/5 = 7385

Cálculo lineal ponderado:

N: La longitud de la media móvil. Pn: El precio para el n-ésimo intervalo. MA: El promedio móvil para el período actual.

FPerc = 2 / (n + 1) MAt = (P x fPerc) + [MA (t-1) x (1 - fPerc)]

MA: El promedio móvil para el período actual. T: El período de tiempo actual.

Cálculo promedio máximo (encontrado debajo de la media móvil 6):

Max Ave. = Suma de (n cierre * n pos ^ pow) / suma de (n pos ^ pow)

N pos. Posición en el período, comenzando en 1 n cerca. Cierre de la barra en pos de potencia: Potencia Media Máxima

Comprar / Vender Señales

Las señales de media móvil se calculan a partir de las primeras 2 líneas de media móvil. Una señal de compra ocurre después de que el promedio móvil se mueve por encima del promedio móvil 2. Se produce una señal de venta después de que el promedio móvil se mueva por debajo del promedio móvil.

Ejemplo de promedios móviles

Preferencias

Para abrir las preferencias de las medias móviles, haga clic en el vínculo rápido (MA) en la parte inferior derecha del gráfico. O puede hacer clic con el botón derecho del ratón, seleccionar Propiedades de superposición y, a continuación, Mover promedios. Si hace clic en el gráfico, la pestaña Preferencias volverá a la configuración del gráfico.

1. Configuración de restauración: TNT Default cambiará su configuración a la configuración original del software. Mi valor predeterminado cambiará la configuración actual a la configuración predeterminada personalizada. Aplicar a todos los gráficos aplicará la configuración seleccionada a todas las superposiciones de promedios móviles en todos los gráficos abiertos. Guardar como predeterminado guardará su configuración personal actual.

2. Cambio de la alternancia media: seleccione esta opción para activar cada línea de media móvil. Hay 6 promedios móviles y una media móvil máxima.

3. Línea: Elija el color, el estilo de línea y el grosor de línea de cada una de sus líneas de promedios móviles.

4. Período: Indica el número de barras que se utilizarán en el cálculo de la media móvil.

* Para agregar un desplazamiento. Agregue un segundo número en el cuadro de período (con sólo un espacio entre los dos números, agregue un signo menos para el desplazamiento negativo). Esto compensa la línea de media móvil dibujada hacia delante o hacia atrás. No se recomienda usar el offset cuando se usan flechas de compra / venta de las primeras 2 medias móviles.

5. Tipo: cambie el tipo de la línea Media móvil a peso simple, lineal o exponencial. Consulte Cálculo arriba para obtener más información sobre cada uno de estos tipos.

6. Datos: Elija entre abierto, alto, bajo o cercano como los datos utilizados en el cálculo de la media móvil.

7. Flechas Compra / Venta: Cambia las flechas de compra / venta para que las primeras 2 medias móviles se muestren o no se muestren. Elija el color de estas flechas. Véase más arriba en las señales de Compra / Venta para saber cómo se calculan. No se recomienda utilizar el desplazamiento de las 2 primeras medias móviles cuando se utilizan estas señales.

8. Alternar Máximo Promedio: Este promedio móvil tiene la línea y el período personalizables, pero sin desplazamiento disponible y sin Tipo o Datos. Para ver cómo se calcula esto, busque el promedio máximo en la sección de cálculo anterior.

9. Potencia media máxima: Ajusta el exponente que usa el cálculo promedio máximo.

Lección 2: Modelos MA, Autocorrelación Parcial, Convenciones de Notación

Lee las notas en línea de Lesson 2 que siguen. (Nota: No hay asignación de lectura del texto esta semana.)

Completa la asignación de la lección 2.

Esta semana estudiaremos una variedad de temas en preparación para la mirada a gran escala de modelos de series de tiempo ARIMA que haremos en las próximas semanas. Los temas de esta semana son modelos de MA, autocorrelación parcial y convenciones de notación.

Después de completar con éxito esta lección, debería ser capaz de:

Identificar e interpretar un modelo MA (q)

Distinguir términos MA de un ACF

Interpretar un PACF

Distinguir términos AR y términos MA de explorar simultáneamente un ACF y PACF

Reconocer y escribir los polinomios AR, MA y ARMA

2.1 Modelos de media móvil (modelos MA)

Un término medio móvil en un modelo de serie temporal es un error pasado (multiplicado por un coeficiente).

El modelo de media móvil de orden 1, denotado por MA (1) es

\ (X_t = \ mu + w_t + \ theta_1w_ \)

El modelo de media móvil de orden 2, denotado por MA (2) es

\ (X_t = \ mu + w_t + \ theta_1w_ + \ theta_2w_ \)

El modelo de media móvil de orden q, denotado por MA (q) es

\ (X_t = \ mu + w_t + \ theta_1w_ + \ theta_2w_ + \ dots + \ theta_qw_ \)

Propiedades teóricas de una serie temporal con un modelo MA (1)

Para los estudiantes interesados, las pruebas de estas propiedades son un apéndice a este folleto.

Ejemplo 1 Supongamos que un modelo MA (1) es x t = 10 + w t + .7 w t-1. Donde \ (w_t \ overset N (0,1) \). Así, el coeficiente θ 1 = 0,7. El ACF teórico está dado por

Una trama de este ACF sigue.

Iid N (0,1). Para esta simulación, sigue un diagrama de series de tiempo de los datos de la muestra. No podemos decir mucho de esta trama.

Propiedades Terapéuticas de una Serie de Tiempo con un Modelo MA (2)

Para el modelo MA (2), las propiedades teóricas son las siguientes:

Iid N (0,1). Los coeficientes son θ 1 = 0,5 y θ 2 = 0,3. Debido a que se trata de una MA (2), el ACF teórico tendrá valores distintos de cero sólo en los retornos 1 y 2.

Los valores de las dos autocorrelaciones no nulas son

A continuación se muestra una gráfica del ACF teórico.

ACF para Modelos Generales MA (q)

Una propiedad de los modelos MA (q) en general es que hay autocorrelaciones no nulas para los primeros q retrasos y autocorrelaciones = 0 para todos los retrasos & gt; Q.

No unicidad de la conexión entre los valores de θ 1 y \ (\ rho_1 \) en el modelo MA (1).

En el modelo MA (1), para cualquier valor de θ 1. El 1 / θ 1 recíproco da el mismo valor para

Como ejemplo, utilice +0.5 para θ 1. Y luego utilice 1 / (0.5) = 2 para θ 1. Obtendrá \ (\ rho_1 \) = 0.4 en ambas instancias.

Invertibilidad de los modelos MA

Invertibilidad es una restricción programada en el software de la serie de tiempo usado para estimar los coeficientes de modelos con términos de MA. No es algo que buscamos en el análisis de datos. En el apéndice se proporciona información adicional sobre la restricción de la invertibilidad para los modelos MA (1).

Código R para los Ejemplos

El primer comando determina el ACF y lo almacena en un objeto llamado acfma1 (nuestra elección de nombre).

Para ver los valores numéricos de la ACF simplemente utilice el comando acfma1.

La simulación y las parcelas se realizaron con los siguientes comandos.

Apéndice: Prueba de Propiedades de MA (1)

Para los estudiantes interesados, aquí hay pruebas de las propiedades teóricas del modelo MA (1).

Variable: \ (\ text (x_t) = \ text (\ mu + w_t + \ theta_1 w_) = 0 + \ text (w_t) + \ text (\ theta_1w_) = \ sigma ^ 2_w + \ theta ^ 2_1 \ sigma ^ 2_w = (1+ \ theta ^ 2_1) \ sigma ^ 2_w \)

Para una serie de tiempo,

Aplique este resultado para obtener el ACF dado anteriormente.

Entonces sustituimos la relación (2) por wt-1 en la ecuación (1)

(3) \ (z_t = w_t + \ theta_1 (z_ - \ theta_1w_) = w_t + \ theta_1z_ - \ theta ^ 2w_ \)

En el instante t-2. La ecuación (2) se convierte en

Entonces sustituimos la relación (4) para wt-2 en la ecuación (3)

\ (Z_t = w_t + \ theta_1 z_ - \ theta_2_1w_ = w_t + \ theta_1z_ - \ theta_2_1 (z_ - \ theta_1w_) = w_t + \ theta_1z_ - \ theta_1 ^ 2z_ + \ theta ^ 3_1w_ \)

Si continuáramos (infinitamente), obtendríamos el modelo de orden infinito AR

\ (Z_t = w_t + \ theta_1 z_ - \ theta ^ 2_1z_ + \ theta ^ 3_1z_ - \ theta ^ 4_1z_ + \ dots \)

Modelo Infinite Order MA

En la semana 3, veremos que un modelo AR (1) se puede convertir en un modelo de orden infinito MA:

\ (X_t - \ mu = w_t + \ phi_1w_ + \ phi ^ 2_1w_ + \ dots + \ phi ^ k_1 w_ + \ dots = \ sum_ ^ \ phi ^ j_1w_ \)

Recordemos en la semana 1, observamos que un requisito para un AR estacionario (1) es que | φ 1 | & Lt; 1. Vamos a calcular el Var (x t) utilizando la representación causal.

Este último paso usa un hecho básico acerca de series geométricas que requiere \ (| \ phi_1 | & lt; 1 \); De lo contrario la serie diverge.

2.2 Función de Autocorrelación Parcial (PACF)

En general, una correlación parcial es una correlación condicional.

Es la correlación entre dos variables bajo la suposición de que conocemos y tomamos en cuenta los valores de algún otro conjunto de variables.

Por ejemplo, considere un contexto de regresión en el que y = variable de respuesta y x 1. X 2. Y x 3 son variables predictoras. La correlación parcial entre y y x 3 es la correlación entre las variables determinadas teniendo en cuenta cómo tanto y como x 3 están relacionados con x 1 y x 2.

En la regresión, esta correlación parcial puede ser encontrada correlacionando los residuos de dos regresiones diferentes: (1) Regresión en la que predice y de x 1 y x 2. (2) regresión en la que se predice x 3 de x 1 y x 2. Básicamente, correlacionamos las "partes" de y y x 3 que no están predichas por x 1 y x 2.

Más formalmente, podemos definir la correlación parcial que acabamos de describir como

Tenga en cuenta que esto es también cómo se interpretan los parámetros de un modelo de regresión. Piense en la diferencia entre interpretar los modelos de regresión:

\ (Y = \ beta_0 + \ beta_1x ^ 2 \ text y = \ beta_0 + \ beta_1x + \ beta_2x ^ 2 \)

En el primer modelo, β 1 se puede interpretar como la dependencia lineal entre x 2 ey. En el segundo modelo, β 2 se interpretaría como la dependencia lineal entre x 2 y y CON la dependencia entre x e y ya explicada.

Para una serie de tiempo, la autocorrelación parcial entre x t y x t-h se define como la correlación condicional entre x t y x t-h. Condicional en x t-h + 1. X t - 1. El conjunto de observaciones que se producen entre los puntos temporales t y t-h.

La autocorrelación parcial de primer orden se definirá para igualar la autocorrelación de primer orden.

La autocorrelación parcial de la 2ª orden (desfase) es

Esta es la correlación entre los valores de dos períodos de tiempo aparte condicionada al conocimiento del valor entre ellos. (Por cierto, las dos variaciones en el denominador serán iguales entre sí en una serie estacionaria.)

La autocorrelación parcial de la 3ª orden (desfase) es

Y así sucesivamente, para cualquier retraso.

Típicamente, las manipulaciones de matriz que tienen que ver con la matriz de covarianza de una distribución multivariante se utilizan para determinar las estimaciones de las autocorrelaciones parciales.

Algunos datos útiles sobre los patrones PACF y ACF

La identificación de un modelo de AR a menudo se hace mejor con el PACF.

Para un modelo AR, el PACF teórico "cierra" pasado el orden del modelo. La frase "se apaga" significa que en teoría las autocorrelaciones parciales son iguales a 0 más allá de ese punto. Dicho de otra manera, el número de autocorrelaciones parciales distintas de cero da el orden del modelo AR. Por el "orden del modelo" nos referimos al retraso más extremo de x que se utiliza como predictor.

Ejemplo. En la lección 1.2, se identificó un modelo AR (1) para una serie temporal de números anuales de terremotos en todo el mundo con una magnitud sísmica mayor de 7,0. A continuación se muestra el ejemplo de PACF para esta serie. Obsérvese que el primer valor de retardo es estadísticamente significativo, mientras que las autocorrelaciones parciales para todos los demás desfases no son estadísticamente significativas. Esto sugiere un posible AR (1) modelo para estos datos.

La identificación de un modelo de MA a menudo se hace mejor con el ACF que con el PACF.

Para un modelo de MA, el PACF teórico no se cierra, sino que se estrecha hacia 0 de alguna manera. Un patrón más claro para un modelo de MA está en el ACF. El ACF tendrá autocorrelaciones no nulas sólo en los retrasos involucrados en el modelo.

La lección 2.1 incluyó la ACF de ejemplo siguiente para una serie MA (1) simulada. Obsérvese que la primera autocorrelación de retardo es estadísticamente significativa, mientras que todas las autocorrelaciones posteriores no lo son. Esto sugiere un posible modelo MA (1) para los datos.

Nota teórica. The model used for the simulation was x t = 10 + w t + 0.7 w t-1 . In theory, the first lag autocorrelation θ 1 /(1+θ 1 2 ) = .7/(1+.7 2 ) = .4698 and autocorrelations for all other lags = 0.

The underlying model used for the MA(1) simulation in Lesson 2.1 was x t = 10 + w t + 0.7 w t-1 . Following is the theoretical PACF (partial autocorrelation) for that model. Note that the pattern gradually tapers to 0.

R note: The PACF just shown was created in R with these two commands:

ma1pacf = ARMAacf(ma = c(.7),lag. max = 36, pacf=TRUE) plot(ma1pacf, type="h", main = "Theoretical PACF of MA(1) with theta = 0.7")

2.3 Notational Conventions

Time series models (in the time domain) involve lagged terms and may involve differenced data to account for trend. There are useful notations used for each.

Using B before either a value of the series x t or an error term w t means to move that element back one time. Por ejemplo,

A “power” of B means to repeatedly apply the backshift in order to move back a number of time periods that equals the “power.” As an example,

$ x_ $ represents x t two units back in time. $B^k x_t = x_ $ represents x t k units back in time. The backshift operator B doesn’t operate on coefficients because they are fixed quantities that do not move in time. For example, Bθ 1 = θ 1 .

AR Models and the AR Polynomial

AR models can be written compactly using an “AR polynomial” involving coefficients and backshift operators. Let p = the maximum order (lag) of the AR terms in the model. The general form for an AR polynomial is

$\Phi(B) = 1-\phi_1B - \dots - \phi_p B^p$.

Using the AR polynomial one way to write an AR model is

iid N(0, σ w 2 ). For an AR(1), the maximum lag = 1 so the AR polynomial is

and the model can be written

$(1-\phi_1B)x_t = \delta + w_t$ .

To check that this works, we can multiply out the left side to get

$x_t - \phi_1x_ = \delta +w_t$.

Then, swing the - φ 1 x t-1 over to the right side and we get

$x_t = \delta + \phi_1x_ +w_t$.

An AR(2) model is $x_t = \delta + \phi_1x_ +\phi_2x_ +w_t$. That is, x t is a linear function of the values of x at the previous two lags. The AR polynomial for an AR(2) model is

The AR(2) model could be written as $( 1-\phi_1B-\phi_2B^2) x_t = \delta + w_t$, or as $\Phi(B)x_t = \delta + w_t$ with an additional explanation that $\Phi(B) = 1-\phi_1B-\phi_2B^2$.

An AR(p) model is $x_t = \delta + \phi_1x_ +\phi_2x_ +. + \phi_p x_ + w_t$, where $\phi_1, \phi_2. \phi_p$ are constants and may be greater than 1. (Recall that $ |\phi_1| < 1 $ for an AR(1) model.) Here x t is a linear function of the values of x at the previous p lags.

A shorthand notation for the AR polynomial is Φ(B) and a general AR model might be written as $\Phi(B)x_t = \delta + w_t$. Of course, you would have to specify the order of the model somewhere on the side.

A MA(1) model $x_t = \mu + w_t + \theta_1 w_ $ could be written as $x_t = \mu + (1+\theta_1B)w_t$. A factor such as $1+\theta_1B$ is called the MA polynomial, and it is denoted as $\Theta(B)$.

A MA(2) model is defined as $x_t = \mu + w_t + \theta_1 w_ + \theta_2 w_ $ and could be written as $x_t = \mu + (1+\theta_1B+\theta_2B^2)w_t$. Here, the MA polynomial is $\Theta(B) = (1+\theta_1B+\theta_2B^2)$.

In general, the MA polynomial is $\Theta(B) = (1+\theta_1B+\dots +\theta_qB^q)$. where $q$ = maximum order (lag) for MA terms in the model.

In general, we can write an MA model as $x_t - \mu = \Theta(B)w_t$ .

Models with Both AR and MA Terms

A model that involves both AR and MA terms might be written $\Phi(B)(x_t-\mu) = \Theta(B)w_t$ or possibly even

Note: Many textbooks and software programs define the MA polynomial with negative signs rather than positive signs as above. This doesn’t change the properties of the model, or with a sample, the overall fit of the model. It only changes the algebraic signs of the MA coefficients. Always check to see how your software is defining the MA polynomial. For example is the MA(1) polynomial 1 + θ 1 B or 1 - θ 1 B?

Often differencing is used to account for nonstationarity that occurs in the form of trend and/or seasonality.

An alternative notation for a difference is

$\nabla x_t = (1-B)x_t = x_t-x_ $.

A subscript defines a difference of a lag equal to the subscript. Por ejemplo,

$\nabla_ x_t = x_t - x_ $.

This type of difference is often used with monthly data that exhibits seasonality. The idea is that differences from the previous year may be, on average, about the same for each month of a year.

A superscript says to repeat the differencing the specified number of times. As an example,

$\nabla^2 x_t = (1-B)^2x_t = (1-2B+B^2)x_t = x_t -2x_ +x_ $.

In words, this is a first difference of the first differences.

Ultimate Moving Average-Multi-TimeFrame-7 MA Types

I just duplicated your exact settings on a JCP daily chart. On top left of screen where it shows the name of the indicator the settings on your chart say (true, D, 20, 1 etc.) That last 1 means it is set to a SMA. if it said 2 that would be EMA, 7 would me TEMA. So I think the issue is when you have the inputs tab open if you change the MA type from 1 to 7 then in real time you see adjustments. But you have to hit OK at the bottom. If you X out on the top right of the tab all the settings will go back to default. which is the setting of 1 which + SMA.

If you still have a problem PM me and we will need to do a screen share. I've verified it works on my end. So if you change the MA type to 7 which equals TEMA MA and then press OK. at the top of screen is should show (true, D, 20, 7) True means use chart resolution, D means the timeframe the MA is calculationg off of, 20 means the period, 1 means the MA Type. so if you change the period from 20 to 50 for example and the MA type from 1 to 2 which is a EMA and press OK. on your screen you should see (true, D, 50, 2 etc.

Please let me know if your still having a issue. I want to get this solved for you

Thank you Chris - much appreciate it your help. I guess I figured out now. I can see now by numbers one can change the type of MA and the timeframe of the chart. Solved:) Thank you from

Indicadores

Wilders Moving Average

Visión de conjunto

Moving averages are amongst the most widely used tools by participants in the currency markets. La fuerza de una media móvil es su capacidad para filtrar el ruido de los precios reduciendo lo que puede ser extremadamente volátil serie de precios en tendencias más discernibles, lo que permite a los comerciantes para determinar la fuerza y la dirección de la tendencia. Los promedios móviles promedian los datos de precios pasados para formar indicadores de tendencias y son un componente en muchos otros indicadores técnicos incluyendo el MACD, el DeMarker y el Sistema de Movimiento Direccional entre muchos otros.

A number of widely used indicators, including the Relative Strength Index (RSI), Average True Range (ATR) and the Directional Movement Index were developed by J. Welles Wilder and introduced in his 1978 book, “ New Concepts in Technical Trading Systems”. Wilder uses a variation of the standard Exponential Moving Average formula, which has a significant impact when choosing suitable time periods for his indicators.

Cálculo

EMA formula = price today * K + EMA yesterday * (1-K) where K = 2 / (N+1)

Wilder EMA formula = price today * K + EMA yesterday (1-K) where K =1/N

Where N = the number of periods.

Trading with Moving Averages

Moving averages are commonly used to identify trends and reversals as well as identifying support and resistance levels. Los promedios móviles como el WMA y el EMA, que son más sensibles a los precios recientes (experiencia menos rezagada con el precio) se volverán antes de un SMA. Por lo tanto, son más adecuados para operaciones dinámicas, que son reactivas a los movimientos de precios a corto plazo. Los promedios móviles, como la SMA, se mueven más lentamente proporcionando información valiosa sobre la tendencia dominante de largo plazo. Sin embargo, pueden ser propensos a dar señales tardías que causan que el comerciante pierda partes significativas del movimiento de precios.

Crossovers medios móviles: El promedio móvil de los crossovers es un término aplicado cuando se usa más de un promedio móvil para generar una señal comercial donde los comerciantes actuarán cuando el promedio móvil a corto plazo cruce el promedio móvil a más largo plazo. A bullish crossover occurs when the shorter term moving average crosses above the longer term moving average (golden cross). Un cruce bajista ocurre donde el promedio móvil más corto del término cruza debajo de la media móvil a largo plazo (cruz muerta).

Crossovers de precios: Un crossover de precios es un término aplicado cuando se genera una señal donde el precio cruza una media móvil. Las señales alcistas se dan cuando el precio se mueve por encima de la media móvil, las señales bajistas se dan cuando el precio se mueve por debajo de la media móvil. Crossover trades are more likely to enjoy success when the moving average slopes are in the direction of the trade.

Soporte y Resistencia: Los promedios móviles también pueden actuar como un nivel de soporte en una tendencia alcista y niveles de resistencia en una tendencia a la baja. Si el promedio se sigue ampliamente, los pedidos a favor de la tendencia a menudo se agrupan alrededor del promedio. Como los mercados son a menudo impulsados por la emoción y muchos jugadores de comercio en contra de la tendencia esperan superaciones, en este sentido el promedio se debe utilizar para identificar el apoyo y las zonas de resistencia en lugar de los niveles exactos.

Moving Average Trade Signals

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MarketDelta Support

Moving Averages - MA

Trevor Harnett 5 июня 2010 г.

Types of moving averages available: Simple, Weighted, Exponential, Wilder, Least Square, Adaptive, Endpoint, Sine-Weighted, Triangular, Modified, Volume Weighted. See examples below.

Moving averages provide different options for smoothing data. Data is smoothed in order to help reduce the effect of bar-to-bar price fluctuations and help identify longer term emerging trends. A moving average reveals the general direction and strength of a stock's price trend over a given period. The term "Moving" is used to refer to the fact that the window of bars that we are considering remain fixed in width (Period) but moves forward with subsequent bar. Some of the averaging methods however are not so much "Moving" as they are "Cumulative" (exponential for one).

The following Price options are available as the input data for each smoothing type: Open, Close, High, Low, HI+LO/2, HI+LO+CL/3, O+H+L+C/4, %Change, or OP+CL/2. In addition, the MA token can be used in RTL to smooth just about anything. For instance, if you wanted to smooth Rate of Change, you would simply use the syntax MA(ROC).

Adaptive Moving Average - This moving average moves slowly when prices are moving sideways and moves swiftly when prices move swiftly.

Triangular Moving Average - The triangular moving average derives its name from the way the weighting factors are applied to the un smoothed data. For example, for a 7 period moving average, the weighting factors are 1, 2, 3, 4, 3, 2, 1. Endpoint Moving Average - The endpoint moving average uses a least squares (linear regression) fit to derive each point on the moving average line based on the preceding period.

Sine-Weighted Average - The sine-weighted moving average is similar in concept to the triangle moving average, but the weighting factors are based on a sine calculation instead.

These new moving averages may be used as overlay indicators showing the moving average of some price type for an instrument, or they may be used as smoothing options in conjunction with other technical indicators. For example, the Adaptive moving average could be used to smooth the CCI, RSI, or MACD indicator.

Simple Moving Average (SMA) - This is probably the most commonly used smoothing type. The Simple method gives equal weighting to each price point over the period considered. Let's assume we are considering a 10-period simple average of the close. The SMA value at each bar will be computed by taking the close of that bar, and the close of the previous 9 (Period - 1) bars, adding them together, and then dividing by 10 (Period), to get the average. Each time you add a new price point to the simple MA, you drop the oldest price point. Simple MA's have a memory of only the last X bars (X being the period).

Exponential Moving Average (EMA) - Exponential averages address two problems that are experienced with Simple Moving Averages: SMAs give equal weight to each price in the period, and SMAs change twice with every new bar (new price added while old price is dropped). The calculation method used by exponential averages is cumulative, meaning that all previous bars have some effect on the EMA value, although that effect diminishes greatly with time. It is similar to other moving averages however in that the smaller the period, the more responsive the MA will be, as the most recent bar will have a greater effect.

EMAs place more weight on recent prices than other moving averages such as SMA. For example, if you choose an EMA period of 7, then the current bar is going to get a weighting factor of 2(n+1) or 2(7+1) in our case, which is 0.25. So the current bar will be weighted 25% while the previous value of EMA (EMA.1) will be weighted 75%. The previous value of EMA is built using each of the previous bars (or prices) to some degree. In a comparable SMA with a period of 7, the current bar and the previous 6 bars all get an equal weighting factor or approximately 14.3% and the bars preceding these 7 bars aren't considered at all. The EMA period is really less of a "period" and more of a conversion factor used in determining the weighting factor or the current bar. Larger periods apply more weighting to past bars, while smaller periods apply more weighting to the current bar (and therefore make the indicator more responsive).

Something else that must be considered when using cumulative indicators such as the EMA, is that the values can change slightly depending on how much data is loaded and considered in the population. This is inherent in the fact that each EMA value considers all past prices to some degree. So if you are using 40 bars to compute the EMA value, then the EMA value of the last bars is based on only those 40 bars, and can be different from an EMA that had 200 prior bars available for calculation. The difference in this case should be rather small and probably insignificant, but this can be an issue when running scans or using custom indicators in custom columns, as MarketDelta optimizes to load the minimum bars necessary. Charts, on the other hand, generally have many more bars at its disposal. This can account for small discrepancies between scan result values and chart values when EMAs are involved.

Beginning in version 5.4.4, MarketDelta has added the ability to allow floating point periods for exponential moving averages. Exponential Moving Average (EMA) has been added as a stand alone technical indicator, and can be reference in RTL with the token EMA. The standard moving average indicator allows only integer values to be used for the period. This new EMA allows numbers such as 2.33, 3.5, or 5.2 to be used as the period. Some traders prefer this option to allow more precise control over the weighting of the current bar.

Weighted Moving Average (WMA) - Weighted MAs share characteristics of both Simple and Exponential Averages. Like Simple MAs, WMA has a fixed window equal to the period specified. In other words, if the period is 10, then only the previous 10 bars will be considered (non-cumulative). Like Exponential MAs, WMA places more emphasis, or heavier weighting, on more recent prices. As can be seen in the formula at the top of this page, the most recent price gets a weighting factor equal to the period. The weighting factor then decreases by 1 for each of the subsequent bars all the way back to a factor of 1 for n - 1 bars back (n being the period).

For comparison, consider a 10 period moving average. For an SMA, the weighting of the current bar would be 10% (1 / 10). For an EMA, the weighting of the current bar would be approximately 18.18% (2 / [10 + 1]). For a WMA, the weighting of the current bar would be approximately 18.2% (10 / [(10 * 11) / 2]).

Volume Weighted Moving Average (VWMA) - The Volume Weighted Moving Average weights the price of each bar with the volume of that bar. In this way, bars with higher volume will be more heavily weighted in the computation of the average. For example, a 5-period VWMA first sum the product of the volume and the price for each of the last 5 bars. This product is then divided by the sum of the volumes to give the resulting average. Many indicators in MarketDelta allow the user to specify the smoothing type. The “Volume Weighted” option can now be found at the bottom of the list of smoothing types. The VWMA can also be accessed in the scan language by simply using the token “MA” and choosing for the smoothing type of the MA to be “Volume Weighted”.

Several preferences of the MA indicator can be adjusted directly from they keyboard without opening up the preference window. First, select the indicator, then use the up and down arrow keys to adjust the smoothing period up or down by 1. To adjust the smoothing type, hold down the shift-key while hitting the up or down arrow keys. It's easy to keep track of the smoothing type by looking at the feedback in the title pane for MA. To adjust the thickness of the MA line, hold down the Ctrl key while hitting the up or down arrow keys. To adjust the floating point EMA indicator, the up and down arrows should also be used. The period is adjusted in increments of 0.1.

Type - Method of calculation used to compute the moving average.

Period - Number of bars used in computation of moving average.

Price - Data value used for computation: Open, Close, High, Low, Hi+Lo/2, Hi+Lo+Cl/3, O+H+L+C/4, %Change, or Op+CL/2

Draw Line. % Above - Check this box to draw a line X percent above the moving average line.

Draw Line. % Below - Check this box to draw a line X percent below the moving average line.

Shift. bars - Check this box if you would like to shift the moving average line right or left X bars.

Draw As - Style and color used to draw the moving average within the chart.

The Moving Average indicator can be referenced in RTL using the token: MA. In addition to the price options available within the MA preferences, the MA token can be used in RTL to smooth just about anything. For instance, if you wanted to smooth Rate of Change, you would simply use the syntax MA(ROC). In this syntax, MA will ignore the price option specified in the preferences and just use the ROC values as input to the smoothing type (and period) specified. The floating point Exponential Moving Average indicator, which allows floating point periods, can be references using the token EMA.

Buy MA Cross MA_Short1 < MA_Long1 AND MA_Short > MA_Long - MA_Short - MA token renamed (Shorter Period) - MA_Long - MA token renamed (Longer Period)

Sell MA Cross MA_Short1 > MA_Long1 AND MA_Short < MA_Long - MA_Short - MA token renamed (Shorter Period) - MA_Long - MA token renamed (Longer Period)

Buy MA Slope Change Up MA > MA.1 AND MA.1 < MA.2

Sell MA Slope Change Down MA < MA.1 AND MA.1 > MA.2

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4 an ma(1) process a moving average process of order

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4 An MA(1) Process A moving average process of order one [MA(1)] can be characterized as one where x t = e t +  1 e t-1. t = 1, 2, … with e t being an iid sequence with mean 0 and variance  2 e This is a stationary, weakly dependent sequence as variables 1 period apart are correlated, but 2 periods apart they are not

5 An AR(1) Process An autoregressive process of order one [AR(1)] can be characterized as one where y t =  y t-1 + e t. t = 1, 2,… with e t being an iid sequence with mean 0 and variance  e 2 For this process to be weakly dependent, it must be the case that | | < 1 Corr( y t, y t+h ) = Cov( y t, y t+h ) /( y y ) = 1 h which becomes small as h increases

6 Trends Revisited A trending series cannot be stationary, since the mean is changing over time A trending series can be weakly dependent If a series is weakly dependent and is stationary about its trend, we will call it a trend-stationary process As long as a trend is included, all is well

7 Assumptions for Consistency Linearity and Weak Dependence A weaker zero conditional mean assumption: E( u t | x t ) = 0, for each t No Perfect Collinearity Thus, for asymptotic unbiasedness (consistency), we can weaken the exogeneity assumptions somewhat relative to those for unbiasedness

8 Large-Sample Inference Weaker assumption of homoskedasticity:

MA Crossovers and Simple Systems - Part 1

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MA means Moving Average

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MA stands for "Moving Average"

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The meaning of MA abbreviation is "Moving Average"

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One of the definitions of MA is "Moving Average"

Moving Average (MA)

Descripción

A moving average creates a series of averages of different subsets. Each new subset remains a constant length by adding the newest value and removing the oldest. A moving average is defined by the user over n-periods of data. This technical indicator along with several others allow the user to select which type of moving average to use in the calculation. Below lists the formula for each type.

Formula

\[Exponential = EMA = (Close_ - EMA_ ) \times k + EMA_ \]

where k = the smoothing constant, equal to $ \frac $

and n = the number of periods in a simple moving average roughly approximated by the EMA

\[Welles\;Wilder Smoothing = WWS_ = WWS_ - \left ( \frac > \right )+(Value_ )\]

where the first calculation of WWS uses a simple moving average $ WWS_ = \frac ^ Close_ > $

Indicadores

Smoothed Moving Average (SMMA)

Visión de conjunto

The SMMA gives recent prices an equal weighting to historic prices. The calculation takes all available data series into account rather than referring to a fixed period. This is achieved by subtracting the prior periods SMMA from the current periods price. Adding this result to yesterday’s Smoothed Moving Average gives today’s Moving Average.

Cálculo

The first value for the Smoothed Moving Average is calculated as a Simple Moving Average (SMA):

SUM1=SUM (CLOSE, N)

The second and subsequent moving averages are calculated according to this formula:

SMMA (i) = (SUM1 – SMMA1+CLOSE (i))/ N

SUM1 – is the total sum of closing prices for N periods; SMMA1 – is the smoothed moving average of the first bar; SMMA (i) – is the smoothed moving average of the current bar (except the first one); CLOSE (i) – is the current closing price; N – is the smoothing period.

Trading with Moving Averages

Moving Average Trade Signals

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How to Choose a Moving Average to Trade With

A trader can choose a moving average based on the time frame that he is trading; the trader might choose to use this indicator on the minute charts, hourly charts, day charts or even weekly.

The trader can also choose to average the closing price, opening price or median price.

Moving average is a commonly used device to measure strength of trends. Los datos son precisos y su salida como una línea se puede personalizar a sus preferencias.

Using the moving average is one of the basic ways to generate buy and sell signals which are used to trade in the direction of the trend, since the MA indicator is a lagging and a trend following indicator and this means that it will tend to give late signals as opposed to leading indicators. However, as a lagging indicator it gives more accurate signals and is less prone to whipsaws compared to leading indicators.

Traders choose the moving average period to use depending on the type of trading they do; short-term, medium-term and long-term.

Short-term: 10 -50 MA Period

Medium-term: 50 - MA 100 Period

Long-term: 100 - MA 200 Period

The period in this case can be measured in minute chart, hourly charts, day charts or even weekly. For our example we will use 1 hour period.

Short term moving averages are sensitive to price action and can spot trends signals faster than the long term ones. Shorter term moving averages are also more prone to whipsaws compared to long term ones and a trader should choose a period that will generate a signal early but not give too many whipsaws.

Long term averages help avoid whipsaws, but are slower in spotting new trends and reversals.

Because long term moving averages calculate the average using more price data, it does not reverse as fast as a short term one and it is slow to catch the changes in the trend. However, the longer term moving average is better when the trend stays in force for a longer time but may also give late trading signals.

The work of a trader is to find a moving average period that will identify trends as early as possible while at the same time avoiding fake-out signals (whipsaws).

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Lesson 1: Moving Averages

Types of Moving Averages

Visión de conjunto

There are several types of moving averages available to meet differing market analysis needs. The most commonly used by traders include the following:

Simple Moving Average

Weighted Moving Average

Promedio móvil exponencial

Simple Moving Average (SMA)

A simple moving average is the most basic type of moving average. Se calcula tomando una serie de precios (o períodos de presentación de informes), sumando estos precios y luego dividiendo el total por el número de puntos de datos.

This formula determines the average of the prices and is calculated in a manner to adjust (or "move") in response to the most recent data used to calculate the average.

Por ejemplo, si incluye sólo los últimos 15 tipos de cambio en el cálculo promedio, la tasa más antigua se eliminará automáticamente cada vez que un nuevo precio esté disponible.

In effect, the average "moves" as each new price is included in the calculation and ensures that the average is based only on the last 15 prices.

Con un poco de prueba y error, puede determinar un promedio móvil que se ajuste a su estrategia comercial. Un buen punto de partida es un promedio móvil simple basado en los últimos 20 precios.

Weighted Moving Average (WMA)

A weighted moving average is calculated in the same manner as a simple moving average, but uses values that are linearly weighted to ensure that the most recent rates have a greater impact on the average.

This means that the oldest rate included in the calculation receives a weighting of 1; the next oldest value receives a weighting of 2; and the next oldest value receives a weighting of 3, all the way up to the most recent rate.

Algunos comerciantes encuentran este método más relevante para la determinación de tendencia, especialmente en un mercado en rápido movimiento.

The downside to using a weighted moving average is that the resulting average line may be "choppier" than a simple moving average. Esto podría hacer más difícil discernir una tendencia del mercado de una fluctuación. Por esta razón, algunos comerciantes prefieren colocar una media móvil simple y una media móvil ponderada en el mismo cuadro de precios.

Candlestick Price Chart with Simple Moving Average and Weighted Moving Average

Exponential Moving Average (EMA)

An exponential moving average is similar to a simple moving average, but whereas a simple moving average removes the oldest prices as new prices become available, an exponential moving average calculates the average of all historical ranges, starting at the point you specify.

Por ejemplo, cuando agrega una nueva superposición de promedio móvil exponencial a un gráfico de precios, asigna el número de períodos de informe que se incluirán en el cálculo. Let's assume you specify for the last 10 prices to be included.

Este primer cálculo será exactamente el mismo que un promedio móvil simple también basado en 10 periodos de informe, pero cuando el próximo precio esté disponible, el nuevo cálculo conservará los 10 precios originales, más el nuevo precio, para llegar al promedio.

Esto significa que ahora hay 11 períodos de informe en el cálculo del promedio móvil exponencial, mientras que el promedio móvil simple se basará siempre en las 10 tasas más recientes.

Deciding on Which Moving Average to Use

To determine which moving average is best for you, you must first understand your needs.

Si su principal objetivo es reducir el ruido de los precios constantemente fluctuantes con el fin de determinar una dirección general del mercado, entonces un promedio móvil simple de las últimas 20 o más tasas pueden proporcionar el nivel de detalle que usted requiere.

Si desea que su media móvil ponga más énfasis en las tasas más recientes, un promedio ponderado es más apropiado.

Tenga en cuenta, sin embargo, que debido a que las medias móviles ponderadas se ven afectadas más por los últimos precios, la forma de la línea media podría distorsionarse potencialmente dando como resultado la generación de señales falsas.

When working with weighted moving averages, you must be prepared for a greater degree of volatility.

Simple Moving Average

Weighted Moving Average

Moving Average Indicator (MA)

Moving Average indicator is one of the most important financial instruments that maximize the trader’s profits. Along with being highly effective, this instrument is very easy to understand and apply. All you need to do is to monitor the direction of the Moving Average line. When the line is moving up, you should buy a Call option. This is when demand is higher than supply. If the line is going down, you should buy a Put option. In this case, supply is higher than demand and the price is expected to continue falling. Moving Average indicator is plotted on the chart as a curve consisting of average price values at certain times. This averaging indicator smoothes out the market’s movements and allows a look at the general picture. Along with the Moving Average line, the chart must also have the trend line. Monitoring the trend line, you can compare the current market movements with the general market direction and avoid false signals.

There are several types of Moving Averages: simple, weighted, smoothed, and exponential. While being very much alike, they have different levels of sensitivity towards market movements. While the Simple Moving Average lags behind, the Weighted Moving Average is extremely sensitive. The perfect option is the Exponential Moving Average which provides reliable data with no excessive market noise.

Moving Averages are a rather flexible instrument that can be successfully adjusted up to your own preferences and requirements. The trader can use several types of Moving Averages simultaneously: one can be used to monitor short-term trends, the second – for medium-term trends, and the third – for long-term trends. To do this, you should set 10,50, and 200 periods, accordingly. Moving Averages provide wide opportunities for trying out new settings and combinations and developing your own strategies.

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Definition of MA Process / Moving Average Process: MA stands for "moving average." Describes a stochastic process (here, e t ) that can be described by a weighted sum of a white noise error and the white noise error from previous periods. An MA(1) process is a first-order one, meaning that only the immediately previous value has a direct effect on the current value:

where p is a constant (more often denoted q ) that has absolute value less than one, and u t is drawn from a distribution with mean zero and finite variance, often a normal distribution.

An MA(2) would have the form:

y así. In theory a process might be represented by an MA(infinity). (Econterms)

Terms related to MA Process / Moving Average Process:

Writing a Term Paper? Here are a few starting points for research on MA Process / Moving Average Process:

Books on MA Process / Moving Average Process: None

Journal Articles on MA Process / Moving Average Process: None

Promedios móviles

References and Further Reading

Kendall MG, Stuart A, Ord JK (1983) Kendall’s advanced theory of statistics. vol 3. Hodder Arnold, London

Ladiray D, Quenneville B (2001) Seasonal adjustment with the X-11 method, vol 158, of Lecture notes in statistics. Springer, Berlin MATH

Makridakis S, Wheelwright SC, Hyndman RJ (1998) Forecasting: methods and applications, 3rd edn. Wiley, New York

Spencer J (1904) On the graduation of the rates of sickness and mortality presented by the experience of the Manchester Unity of Oddfellows during the period 1893–1897. J Inst Actuaries 38:334–343

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Media móvil

As the Technical Analysis arsenal evolves, there are now countless indicators available and the number is still increasing as you read this post. Despite that fact, I can confidently say that few have proved to be useful and reliable as the Moving Average(MA).

1) Type of Moving Average

There are 4 types of Moving Average as far as I know: namely Simple, Exponential, Smoothed, and Linear Weighted.

To be honest I don’t even know how the last 2 are calculated^^ Simple Moving Average(SMA): Check out the video here Exponential Moving Average(EMA): Same video above.

The Simple MA is slower and more stable. On the other hand, the Exponential MA reacts faster to price change as it put more weight on the latest prices.

2) Choose type of price to calculate the Moving Average:

As we discuss in the Candlestick chapter, there are always 4 types of price available: high, low, open and close. The majority of traders use the close price for Moving Average and actually for all other indicators.

I personally use close price to plot any indicators in my trading. Hence, my suggestion for the newbie is definitely the Close Price. Over time when you become familiar with the market, you can try to test everything you like but for now to keep it simple and save you the time to learn some much more valuable knowledge, JUST USE THE CLOSE PRICE !

3) Choosing the day period

You are encouraged to try adjust the period to fit your trading flavors :D. One hint is that some traders love to use the period which is a Fibonacci number ( 5,21,55 etc..) Here is my recommendation for each market:

US Stock Market: SMA 20, SMA 40, EMA 55 VietNam Stock Market: SMA 5, SMA 10, SMA20 Forex market: EMA 21, EMA 55.

MA with lower period days tend to react much quicker to the market compared to the high period MA. Hence, we often call MA with lower period Fast MA and slow MA for the higher period MA. ** On financial media, we often see the presence of MA 200 days. It is only used for a very long-term strategy but I personally don’t like to use a lagging indicator in the long-term as Fundamentals rule everything in the long-term not a lagging indicator.

4) Moving average acts as support and resistance

The most important application of Moving Average is the provision of support during the uptrend and resistance during the downtrend. In turn, Moving Average provides a relatively good entry point for our trade. Let’s have a look at an example:

Figure 1 is HPQ Daily chart with an Simple MA 40 days. You can see the price bounces back up every time it touches the MA. If you are planning to jump in the market and ride the trend then all the red arrows are the good points to get entry.

And just like every support, we will have a resistance once a support is broken. Just scroll back the chart a few years. This is the HPQ Daily chart with a downtrend. You can see the resistance force provided by the MA. Points marked with red arrows are good entry for short position.

So why we need to take the entry near a support? The answer is very simple. If you buy or sell at a random point in the trend, you might end up seeing price run against your position in a few weeks (Look at points marked with A on the above examples). After that price might be luckily back in your direction but it is only after some heart palpitation and some protective stop being triggered. Trading is about avoiding pain so don’t give yourself some sleepless nights with a random entry point. Believe me, even with a good strategy, you still probably can’t handle the stress and anxiety in this market so don’t start the trading career with some stupid random entry point :D.

5) Moving Average Cross Over

Using the support and resistance from MA can only give you the reward which is a part of the trend. If you are kind of risk-taking traders, you might want to consider aggressively buy and sell on the MA crossover, which in turn will give you a tremendously profitable trade in a trending market.

Strategy: We will plot 2 MA on the chart. One with lower days period (the faster one). In the next example I will use SMA (20 days - green) and SMA (40days-violet).

Buy signal: When the faster MA cross the slow MA from the below. Sell signal: When the faster MA cross the slow MA from the above.

Look at the example below. Who love Nike shoes :p. Indeed, the chart below is Nike daily chart. You can see how profitable can a trade be if we act on MA Crossover signal.

6) Convergence and Divergence

There is one more thing, which is not reliable about MA but has been talked about by some traders online. It is when the faster MA moves too ‘fast’ and make abnormally big vertical distance with the slow MA, the market is expected to correct the fast MA back to near the slow MA. There is a problem with this application. It is unclear how much big is abnormally big. Hence this is not a good way to use MA in. Just read for your own knowledge but be careful before using it.

7) When the MA won’t work?

By now, the example of NIKE stock might be already giving you a feeling of wealth and rich lol. It’s time to get back to the ground and know the risk we will be facing when take the entry with MA crossover.

When the market doesn’t trend in any direction, it’s the time we can say good bye to MA lol. Let’s look at Mark Zuckerberg ‘s company 😀

FB stock trends sideway (choppy) for 4 months. Anyone try to buy and sell on MA Cross over signal will end up with a loss for sure. The power of MA is to ride the trend and now we see no trend. too bad !

Ok so you might now start thinking “Hey Whirlpool, you talk too much! Now show us what we should do with the MA Cross Over strategy”. What I can tell from my experience with this strategy is that you need the courage to bear all the loss when the market trend sideways ( which is just some small loss) to wait for a big fish ( when the market does trend). History has proven that trend riding strategy was, is and will always be the most profitable one in the whole TA. The only hard part of the strategy is the requirements of patience and courage to stand still when the market trend sideways.

Análisis técnico

moving_average v3.1 (Mar 2008)

MOVING_AVERAGE(X, F) smooths the vector data X with a boxcar window of size 2F+1, i. e. by means of averaging each element with the F elements at his right and the F elements at his left. The extreme elements are also averaged but with less data, obviously. Leaving the edges intact. The method is really fast.

MOVING_AVERAGE2(X, M,N) smooths the matrix X with a boxcar window of size (2M+1)x(2N+1), i. e. by means of averaging each element with its surrounding elements that fits in the mentioned box centered on it. This one is also really fast. The elements at the edges are averaged too, but the corners are left intact.

NANMOVING_AVERAGE(X, F) or NANMOVING_AVERAGE(X, F,1) accept NaN's elements in the vector X; the latter interpolates also those NaN's elements surrounded by numeric elements.

NANMOVING_AVERAGE2(X, M,N) or NANMOVING_AVERAGE2(X, M,N,1) accept elements NaN's in the matrix X; the latter interpolates also those NaN elements surrounded by numeric elements.

[ New simple GAP filling ]: SMOOTH_MAVERAGE(X, M,N, IND) this one smooths only the X(IND) elements. ignoring NaNs. This can be used to elimante GAPS on your data.

Each M-files has an example (see the screenshot).

Check below to see the CHANGES on v3.1.

Note: Looking the 2 dimensional code from MOVING_AVERAGE2.M (and RUNMEAN for some hints) somebody can easily make an N-dimensional MA. Lo harías?

MATLAB 7.5 (R2007b)

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Comments and Ratings (31)

I would like to get a moving average function dealing with nan values

Carlos, I like your function moving_average, very easy to use. I have data which has small to large time gaps and I don't want to filter across the gaps. I could break the vector up at each gap but that would mean work. Any suggestion on how to handle something like this?

Very useful foe me (mainly for plotting)

Dear all, I'm dealing with gap filling on weather measurements which the NaN should be filled based on the time window of several days.(i. e. neighborhood hour of several days).

For example, one NaN at 5pm will be replaced by the mean value in the neighborhood hour of neighborhood several days. (let's say 4, 5 and 6pm of neighborhood 5 days)

Here is the bone of question I like to deal with:

values = rand(1,1000)'; fake_NaN = floor(rand(1,300)'*1000); values(fake_NaN) = NaN; for i = 1:length(values) n = 24 * i * (1:5) having_nan_index = find(isnan(values)) new_values = nanmean(values(having_nan_index * n-1:having_nan_index*n+1)) : : Something like that : :

If you have any solutions or advices, please feel free to let me know. Thanks, Michael

hi Carlos i have send you an email about the difficulties in programmation of the recursive moving coverage have you any idea about this issue? any help please? thanks by advance

Edgar Guevara Codina

It's adequate por postprocessing of spectroscopic signals, quite useful indeed.

Carlos Adrian Vargas Aguilera

Common Aslak, you are searching for FLEAS instead of BUGS. But, ok, USERS: BEWARE of OUTLIERS and LARGE MEANS when using CUMSUM runmean method! Rather use: NDNANFILTER :)

Hi Carlos. I meant it as a constructive criticism. The point is that the error is unnecessary, easily avoidable, and there is no speed advantage. You are right that in the specific example the error is not very big (although you make the mistake of comparing it to the mean rather than the standard deviation). However, just because the error is small in that case does not mean it is for all series. Try for example this:

m=3; n=100000; x=randn(n,1); x(1)=1e100;

The problem is that the outlier gives rise to huge errors in the whole smoothed series, and not just within the window.

I forget the rating for Aslak's example (1 star): he is comparing errors of precisions 1e-9=0.000000001 and 1e-13

eps. Yes 10,000 times greater, but for values with 1,000 mean which is 1'000,000'000,000 greater than the greater error. That is a great little error isn't it?

Nice code but. The cumsum trick to calculate moving averages can result in unneccarily large errors under certain conditions: * The mean is very different from zero and the series is very long.

Here's a small test that illustrates the problem by using 3 different approaches of calculating the moving average. It shows that the 'cumsum' method has errors that are more than 10000 times greater than the errors from the filter method. There is no real speed difference.

m=10; n=300000; x=randn(n,1)+1000; %think for example atmospheric pressure.

tic s=nan(length(x)-m+1,1); for ii=1:length(s) s(ii)=mean(x(ii+(0:m-1))); end slowtime=toc

tic; c=[0;cumsum(x)]; c=(c(m+1:end)-c(1:end-m))/m; cumsumtime=toc cumsumerror=sqrt(mean((c-s).^2))

tic; flt=ones(m,1)/m; f=filter2(flt, x,'valid'); filtertime=toc filtererror=sqrt(mean((f-s).^2))

slowtime = 9.4732 cumsumtime = 0.041549 cumsumerror = 2.6456e-009 filtertime = 0.033685 filtererror = 1.4151e-013

Well commented Check I/O numbers and errors vectorized quick

Carlos Adrián Vargas Aguilera

Found a harmless bug on MOVING_AVERAGE, line 75: extra comma in the warning! ja!

R K: In fact, those are limitations of this moving average, but the problem with the edges are common in filtering theory. The author provides us an idea and you?

BTW: that GAP filling is what i was looking for. ¡Gracias!

Carlos Adrián Vargas Aguilera

Hello Sam! Gracias por tus comentarios. I had no problem with the example, you should get the screenshot above (without the holes), maybe it's your matlab release but the code is really simple and should work on others.

About the F, to get a centered average around an element, the number of elements to average should be odd, so 2F+1, and in this way F is the half-width of the window (check the Description above). Similar for the m, n on 2D.

Hi Carlos, thank you so much for your interesting matlab code. I have one doubt about the window size in 1D moving average. The size of the window is '2F+1' can you please tell me what 'F' stand for?

Also I have tried to get the 2D moving average to work with your supplied example, i couldn't get it to work.

Documentación

Moving Average Model

MA( q ) Model

The moving average (MA) model captures serial autocorrelation in a time series y t by expressing the conditional mean of y t as a function of past innovations, ε t − 1. ε t − 2. …. ε t − Q. An MA model that depends on q past innovations is called an MA model of degree q . denoted by MA( q ).

The form of the MA( q ) model in Econometrics Toolbox™ es

y t = c + ε t + θ 1 ε t − 1 + … + θ q ε t − Q.

where ε t is an uncorrelated innovation process with mean zero. For an MA process, the unconditional mean of y t is μ = c .

In lag operator polynomial notation, L i y t = y t − yo. Define the degree q MA lag operator polynomial θ ( L ) = ( 1 + θ 1 L + … + θ q L q ). You can write the MA( q ) model as

y t = μ + θ ( L ) ε T

Invertibility of the MA Model

By Wold's decomposition [1]. an MA( q ) process is always stationary because θ ( L ) is a finite-degree polynomial.

For a given process, however, there is no unique MA polynomial—there is always a noninvertible and invertible solution [2]. For uniqueness, it is conventional to impose invertibility constraints on the MA polynomial. Practically speaking, choosing the invertible solution implies the process is causal . An invertible MA process can be expressed as an infinite-degree AR process, meaning only past events (not future events) predict current events. The MA operator polynomial θ ( L ) is invertible if all its roots lie outside the unit circle.

Econometrics Toolbox enforces invertibility of the MA polynomial. When you specify an MA model using arima. you get an error if you enter coefficients that do not correspond to an invertible polynomial. Similarly, estimate imposes invertibility constraints during estimation.

Referencias

[1] Wold, H. A Study in the Analysis of Stationary Time Series . Uppsala, Sweden: Almqvist & Wiksell, 1938.

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Moving Average Processes¶

As with the $\smash $ :

\[\begin \begin \text [Y_t] & = \text [\mu + \varepsilon_t + \theta_1 \varepsilon_ + \ldots + \theta_q \varepsilon_ ] \\ & = \mu + \text [\varepsilon_t] + \theta_1 \text [\varepsilon_ ] + \ldots + \theta_q \text [\varepsilon_ ] \\ & = \mu. \end \end \]

$\smash $ Autocovariances¶

\[\begin \begin \gamma_j & = \text \left[(Y_t-\mu)(Y_ -\mu)\right] \\ & = \text \big[(\varepsilon_t + \theta_1\varepsilon_ + \ldots + \theta_q \varepsilon_ ) \\ & \hspace \times (\varepsilon_ + \theta_1\varepsilon_ + \ldots + \theta_q \varepsilon_ )\big]. \end \end \]

For $\smash $. all of the products result in zero expectations: $\smash $. for $\smash $ .

For $\smash $. the squared terms result in nonzero expectations, while the cross products lead to zero expectations:

\[\smash [\varepsilon^2_t ] + \theta^2_1 \text [\varepsilon^2_ ] + \ldots + \theta^2_q \text [\varepsilon^2_ ] = \left(1 + \sum_ ^q \theta^2_j\right) \sigma^2.>\]

$\smash $ Autocovariances¶

\[\begin \begin \gamma_j & = \theta_j\text [\varepsilon^2_ ] + \theta_ \theta_1 \text [\varepsilon^2_ ] \\ & \hspace + \theta_ \theta_2 \text [\varepsilon^2_ ] + \ldots + \theta_ \theta_ \text [\varepsilon^2_ ] \\ & = (\theta_j + \theta_ \theta_1 + \theta_ \theta_2 + \ldots + \theta_q\theta_ ) \sigma^2. \end \end \]

The autocovariances can be stated concisely as

\[\begin \begin \gamma_j & = \begin (\theta_j + \theta_ \theta_1 + \theta_ \theta_2 + \ldots + \theta_q\theta_ ) \sigma^2 & \text j = 0, 1, \ldots, q \\ 0 & \text j > Q. \end \end \end \]

$\smash $ Autocorrelations¶

BMA MetaTrader indicator or Band Moving Average — was created by using the original moving average indicator and the idea from one of the site's visitors. The indicator displays itself in the form of three lines: the central one is the standard MT4/MT5 moving average (which can be simple, exponential or weighted), the upper line is the same as the central one but lifted up by 2% (by default), the lower line is the same as the central one but pushed down by 2%. Those two additional lines serve as the support and resistance levels. El indicador está disponible para MT4 y MT5.

Parámetros de entrada:

MA_Period (default = 49) — the period of the standard moving average (central line).

MA_Shift (default = 0) — horizontal shift for all lines on the chart.

MA_Method (default = 0) — the method for MA drawing. 0 — simple moving average, 1 — exponential, 2 — smoothed, 3 — weighted.

Percentage (default = 2) — number of percents to vertically shift the upper and lower bands compared to the central line.

The best way to use this indicator is to attach it to EUR/USD H4 chart (shown in example) and to sell when the price reaches upper band and to buy when the price reaches lower band. Moderate stop-loss level is advised in both cases as the price can sometimes break those levels or the lines may change directions suddenly.

Descargas:

Discussion:

¡Advertencia! Before you ask any basic questions regarding installation of the indicators, please, read this MT4 Indicators Tutorial to get the elementary knowledge on handling them.

Do you have any suggestions or questions regarding this indicator? You can always discuss BMA with the other traders and MQL programmers on the indicators forums.

Moving Average (MA)

Los promedios móviles son una de las herramientas técnicas más utilizadas. They follow the trend, smooth the normal fluctuations of the data, and clearly signal long and short positions to the investor.

This study displays moving averages as the normal crossover trading system. You may select up to three different averages.

Most investors and charting services use three moving averages. Their lengths typically consist of short, intermediate, and long-term. A commonly used system is 4, 9, and 18 intervals. An interval may be ticks, minutes, days, weeks, or even months; it depends upon the chart type.

The normal moving average crossover buy/sell signals are as follows. A buy signal is flashed when the short and intermediate term averages cross from below to above the longer term average. Por el contrario, se emite una señal de venta cuando los promedios a corto y medio plazo se cruzan desde arriba hasta por debajo del promedio a más largo plazo.

You can use the crossover approach with only two moving averages, but market technicians suggest longer term averages (a longer interval) when trading only two moving averages in a crossover system.

PARAMETERS:

Period1 (4) - the number of bars, or interval, used to calculate the first moving average.

Period2 (9) - the number of bars, or interval, used to calculate the second moving average.

Period3 (18) - the number of bars, or interval, used to calculate the third moving average.

COMPUTATION .

The formula to calculate a moving average is as follows:

Mat = (P1 +. + Pn) / n

Mat is the moving average for the current period,

Pn is the price for the nth interval

n is the length of the moving average.

Zaner computes the average of the past n intervals using the price specified for that period. Now use real values to compute a five interval moving average. If you assume the following prices, the calculations are: MA = (7380 + 7375 + 7385 + 7390 + 7395) / 5 = 36925 / 5 = 7385 As you can see, it is a simple process. It does become rather tedious as you repeat this process several hundred times for a single moving average. That is why you have Zaner. It does the work, and you perform the analysis.

The Moving Average technical indicator shows an average price value for a certain period of time. Calculating the moving average, one makes price averaging for this time period. As the price changes, its moving average either increases or decreases.

There are four different types of moving averages: Simple (also referred to as arithmetic, exponential, smoothed and linear weighted. With the help of moving averages any sequential data set may be calculated, including opening and closing prices, highs and lows, trade volume or any other indicators. Double moving averages are also used often.

Weight coefficient of latest data is the only thing that distinguishes moving averages of different types. In case of simple moving average, all prices in the given time period are equal in value. Exponential and linear weighted moving averages attach more value to the latest prices.

The most common way to interprete the price moving average is to compare its dynamics to the price action. When an asset's price rises above its moving average, a buy signal appears; if the price falls below its moving average, what we have is a sell signal.

This kind of trading system based on the moving average is not designed to provide market entries right in its lowest point and exits right on the peak. It allows a trader to act according to the following trend: to buy soon after the prices reach the bottom, and to sell soon after the prices have reached their peak.

Los promedios móviles también pueden aplicarse a los indicadores. That is where the interpretation of indicator moving averages is similar to the interpretation of price moving averages: if the indicator rises above its moving average, that means that the ascending indicator movement is likely to continue. If the indicator falls below its moving average, this means that it is likely to continue going downward.

Here are the types of moving averages on the chart:

Simple Moving Average (SMA)

Exponential Moving Average (EMA)

Smoothed Moving Average (SMMA)

Linear Weighted Moving Average (LWMA)

Calculation:

Simple Moving Average (SMA)

Simple or arithmetical moving average is calculated by summing up the prices of instrument closure over a certain number of single periods (for instance, 12 hours). Este valor se divide entonces por el número de tales períodos.

SMA = SUM(CLOSE, N)/N

N - is the number of calculation periods.

Exponential Moving Average (EMA)

Exponentially smoothed moving average is calculated by adding the moving average of a certain share of the current closing price to the previous value. Con los promedios móviles suavizados exponencialmente, los últimos precios son de mayor valor. P-percent exponential moving average will look like:

CLOSE(i) - the price of the current period closure;

EMA(i-1) - Exponentially Moving Average of the previous period closure;

P - the percentage of using the price value.

Smoothed Moving Average (SMMA)

The first value of this smoothed moving average is calculated as the simple moving average (SMA):

SUM1 = SUM(CLOSE, N)

The second and succeeding moving averages are calculated according to this formula:

SUM1 - is the total sum of closing prices for N periods;

SMMA1 - is the smoothed moving average of the first bar;

SMMA(i) - is the smoothed moving average of the current bar (except for the first one);

CLOSE(i) - is the current closing price;

N - is the smoothing period.

Linear Weighted Moving Average (LWMA)

In the case of weighted moving average, the latest data is of more value than more early data. Weighted moving average is calculated by multiplying each one of the closing prices within the considered series, by a certain weight coefficient.

LWMA = SUM(Close(i)*i, N)/SUM(i, N)

SUM(i, N) - is the total sum of weight coefficients.

Triangular Moving Average (TriW-MA)

The Triangular Weighted Moving Average (TriW-MA) is included in the ‘Technical Indicator – Fight for Supremacy ‘ so before we test it here is some information on how it is calculated. If you would like to use the Triangular Moving Average in Excel then you can download a free spreadsheet HERE .

The TriW-MA gets it name from the way it applies the weight to data; because the emphasis is on the values in the middle, the weighting takes the shape of a triangle. Below you can see how the weighting is applied to a 50 period TriW-MA, EMA and SMA :

How To Calculate a Triangular Weighted Moving Average

To calculate a Triangular Weighted Moving Average multiply each close price by the weight for that period, add it all up and divide the result by the sum of the weights. The weighting multiplier starts at 1 and increases by 1 until it peaks half way through the set before decreasing symmetrically back down to finish at 1 again.

Here is an example of a 3 period Triangular Weighted Moving Average:

The same result can be achieved by using a double smoothed moving average AKA the Triangular Simple Moving Average .

Triangular Weighted Moving Average Excel File

An Excel Spreadsheet containing a Triangular Weighted Moving Average is available for FREE download. It contains the ‘basic’ version you can see above and a ‘fancy’ one that will automatically adjust to the length you specify. Find it at the following link near the bottom of the page under Downloads – Technical Indicators: Triangular Weighted Moving Average (TriW-MA). Please let us know if you find it useful.

Triangular Moving Average and a Simple Moving Average

Test Results

We tested several different types of Weighted Moving Averages including the TriW-MA through 300 years of data across 16 global markets to reveal which is the best and if any of them are worth using in your trading systems. See the results – Weighted Moving Averages Put To The Test

Stocks Screen: 50 Day Moving Average Bounce Candidates

July 19, 2011 2:26 pm

We looked to find some potential bounce candidates that are nearing their 50 Day Moving Average. Below are a list of the tickers, description and the criteria for screening:

All United States Exchanges Average Daily Volume > 700,000 Price > $8.00 Price 3 Months Ago < Current Price (Establishes that stock is in an uptrend) Price 2 Weeks Ago is > Current Price (Establishes that stock is in a short-term pull back) 50 Day MA < Price < 50 Day MA*1%+50 Day MA (This basically says that the price is between the 50 Day Moving average and 1% above the 50 Day Moving Average.

Scroll down to see a chart of these stocks on this screen. Click to enlarge

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Moving Average (MA) – It is an average of data for a certain number of time periods. As it “moves” due to each calculation, we use the latest N number of time periods’ datos. By definition, a moving average lags the market. The Simple Moving Average gives equal weight to each N number of values, whereas the rest of the Moving Averages give greater weight to the more recent data, in an attempt to reduce the lag.

There are five different types of moving averages: Simple, Exponential, Smoothed, Linier Weighted and Adaptive Moving Averages. Any of the Moving Averages may be calculated for any sequential data set, including opening and closing prices, highest and lowest prices, volume or any other indicators.

Lo único en que los promedios móviles de diferentes tipos divergen considerablemente entre sí, es cuando los coeficientes de peso, que se asignan a los últimos datos, son diferentes. In case we are talking of simple moving average, all prices of the time period in question are equal in value. The Other Moving Averages attach more value to the latest prices.

La forma más común de interpretar el precio promedio móvil es comparar su dinámica con la acción del precio. Cuando el precio del instrumento sube por encima de su promedio móvil, aparece una señal de compra, si el precio cae por debajo de su media móvil, lo que tenemos es una señal de venta.

This trading system, which is based on the moving average, is not designed to provide entrance into the market neither right at its lowest point nor its exit right on the peak. It allows acting according to the following trend: to buy soon after the prices reach the bottom and to sell soon after the prices have reached their peak.

Los promedios móviles también pueden aplicarse a los indicadores. Es ahí donde la interpretación de las medias móviles de los indicadores es similar a la interpretación de los promedios móviles de los precios: si el indicador sube por encima de su media móvil, es probable que continúe el movimiento del indicador ascendente: si el indicador cae por debajo de su promedio móvil, Significa que es probable que siga bajando.

CALCULATIONS

SIMPLE MOVING AVERAGE (SMA)

Simple, in other words, arithmetical moving average is calculated by summing up the prices of the instrument over a certain number of single periods; N . Este valor se divide entonces por el número de tales períodos.

Dónde:

N — is the number of calculation Periods; Price(i) — The price of the i’te period. 0 is the most recent period

Exponential Moving Average (EMA)

Exponential moving average is calculated by adding the moving average of a certain share of the current price to the previous value. With exponentially moving averages, the latest prices are of more value. P - percent exponential moving average will look like:

Dónde:

N — is the number of calculation Periods; Price(0) — the price of the current period; EMA(1) — Exponentially Moving Average of the previous period; P — the percentage of using the price value.

Smoothed Moving Average (SMMA)

The smoothed moving average is calculated cording to this formula:

Dónde:

SMMA(1) — is the smoothed moving average of the previous bar; N — is the smoothing period.

Linear Weighted Moving Average (LWMA)

Dónde:

N – is the smoothing period. Price(0) – the price of the current period. Price(i) – the price of the I’te period ago

Smoothing Method

Once you have selected the Moving Average(MA) method to be used in the calculation, you need to select the Smoothing Method . as shown in Figure 1:

The three options are:

The graph below displays all the 3 above mentioned methods applied:

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Price vs. 50 Day Moving Average (%)

What is the definition of % 50d MA .

This measures how far the last close price is from the 50 Day Moving Average. The 50 Day Moving Average is a stock price average over the last 50 days which often acts as a support or resistance level for trading.

This is calculated as (Close Price - 50 Day MA) / 50 Day MA * 100.

Stockopedia explains % 50d MA .

The 50 Day Moving Average is a stock price average over the last 50 days which often acts as a support or resistance level for trading. The moving average will trail the price by its very nature. As prices are moving up, the moving average will be below the price, and when prices are moving down the moving average will be above the current price. If the short term (50 day) Moving Average breaks above the long-term (200 Day) Moving Average, this is known as a Golden Cross, whereas the inverse is known as a Death Cross. As long-term indicators carry more weight, the Golden Cross may indicates a bull market on the horizon and is usually reinforced by high trading volumes.

Which Guru Screens is % 50d MA used in?

Media móvil

Mulai dari chapter ini Anda akan mempelajari indikator teknikal. Perlu Anda ketahui bahwa indikator teknikal bukanlah alat yang bisa menjadikan Anda seperti cenayang. Indikator teknikal hanya membantu Anda untuk mengenali potensi pergerakan harga.

Kali ini Anda akan mempelajari indikator teknikal yang bernama Moving Average. Moving average (selanjutnya akan kita sebut sebagai MA) merupakan salah satu indikator tren yang cukup populer. Indikator ini “memperhalus” pergerakan harga dalam rentang waktu tertentu, sehingga Anda dipermudah untuk mengenali tren atau arah pergerakan harga secara umum. Mari kita lihat gambar berikut ini.

Gambar di atas adalah grafik 1 jam-an AUD/USD. Garis berwarna merah yang terlihat grafik tersebut adalah salah satu contoh indikator moving average yang memiliki periode 50 (MA 50). Artinya, indikator tersebut mengambil data harga dari 50 candlestick terakhir, lalu menggambarkannya sebagai garis yang Anda lihat itu. Standar harga yang digunakan biasanya adalah harga penutupan (close), namun ada beberapa metode yang menggunakan harga open, high, atau low. Namun kita tidak akan membahas hal tersebut kali ini.

Kembali ke gambar di atas, Anda bisa melihat bahwa MA bisa memperlihatkan kepada Anda tren yang sedang berlangsung. Jika harga pada umumnya berada di bawah MA, maka tren saat itu adalah downtrend.

Sebaliknya, jika harga secara umum bergerak di atas MA, maka tren saat itu adalah uptrend. Dari contoh di atas terlihat bahwa trend untuk AUD/USD pada grafik 1 jam-an (hourly) adalah turun (downtrend). Semakin curam kemiringan MA tersebut, maka itu artinya tren yang terjadi semakin kuat. Dengan demikian, Anda bisa lebih mudah memperkirakan potensi arah pergerakan selanjutnya.

MA juga bisa berfungsi sebagai support dan resistance. Istilahnya adalah support dan resistance dinamis (dynamic support and resistance) . Dinamakan demikian karena ia bergerak sesuai dengan pergerakan harga.

Pada saat uptrend, MA berfungsi sebagai support. Sebaliknya pada saat downtrend, MA berfungsi sebagai resistance.

Oke, mungkin Anda sudah tidak sabar ingin segera mencicipi resep trading menggunakan MA ini. Sabar… bahkan Utut Adianto juga belajar dasar-dasar catur dulu kok sebelum menjadi Grand Master.

Baiklah, kita akan segera melangkah lebih jauh lagi.

Dalam pembelajaran mengenai MA ini, Anda hanya akan membahas dua jenis MA yang populer saja, yaitu:

Simple Moving Average (SMA)

Exponential Moving Average ( EMA)

Anda akan mempelajari dasar-dasarnya dulu, baru nanti Anda akan pelajari strateginya. Oke, ini dia….

Simple Moving Average (SMA)

Simple Moving Average (SMA) ini merupakan MA yang paling sederhana. Ya, sesuai dengan namanya: simple. Tapi jangan remehkan kemampuan si SMA yang sederhana ini, karena dengan penggunaan yang tepat ia pun bisa menuntun Anda untuk mengenali pergerakan harga.

Jika Anda menggunakan SMA 50 di grafik 1 jam-an, maka SMA 50 yang Anda lihat adalah hasil dari penjumlahan 50 harga penutupan terakhir, lalu hasil penjumlahan itu dibagi lagi dengan 50. Dari perhitungan itulah Anda bisa memperoleh nilai rata-rata dari harga penutupan dalam 50 jam terakhir.

Sudah dapat gambarannya kan? Oke, kita lanjutkan.

Seperti yang pernah disampaikan, pada prakteknya Anda tidak perlu susah-susah lagi menghitung SMA ini, platform trading yang Anda gunakan sudah menyediakan alatnya. Lho, lalu mengapa repot-repot mempelajari perhitungannya? Tujuannya hanya agar Anda memiliki gambaan mengenai apa sebenarnya SMA ini. Juga agar Anda memiliki dasar jika nanti Anda ingin memodifikasi SMA ini sesuai dengan strategi Anda nantinya.

Seperti yang telah disampaikan di awal tadi: MA “memperhalus” pergerakan harga. Semakin besar periode yang digunakan maka semakin “halus” pula MA yang dihasilkan. Semakin halus MA yang dihasilkan maka akan semakin lambat ia bereaksi terhadap pergerakan harga.

Mari kita lihat perbandingan antara SMA 20 dengan SMA 50 berikut ini.

Nah, kelihatan kan? SMA 20 yang berwarna biru memiliki liukan-liukan yang lebih agresif dibandingkan dengan SMA 50 yang berwarna merah. Ini menunjukkan bahwa SMA 20 yang memiliki periode lebih pendek lebih cepat bereaksi terhadap pergerakan harga, sedangkan SMA 50 cenderung lebih lambat daripada SMA 20. SMA 50 terlihat lebih “kalem”, tidak se-“liar” SMA 20.

Dengan mengamati kedua SMA di atas Anda bisa melihat bahwa pasar tengah dalam keadaan trending. Kedua SMA yang Anda lihat pada grafik di atas menggambarkan arah tren secara umum, yaitu downtrend.

Pada topik yang lebih lanjut Anda akan mempelajari strategi penggunaan SMA ini, kelemahannya serta cara mengantisipasi kelemahan SMA tersebut.

Exponential Moving Average (EMA)

Perhitungan EMA tidaklah sesederhana SMA. EMA memberikan bobot yang lebih dalam perhitungan harga rata-rata dalam rentang waktu tertentu. Efeknya adalah EMA cenderung lebih sensitif terhadap pergerakan harga. sehingga EMA bergerak sedikit lebih agresif daripada SMA.

Gambar di atas memperlihatkan SMA dan EMA yang diplot pada grafik yang sama. Periode yang digunakan juga sama-sama 50 namun metode perhitungannya berbeda. MA yang berwarna biru adalah EMA, sedangkan MA yang berwarna merah adalah SMA. Anda bisa melihat bahwa EMA 50 selalu lebih dekat kepada SMA 50. Ini artinya EMA lebih merepresentasikan pergerakan harga (price action) daripada SMA. Dengan kata lain, EMA lebih menggambarkan apa yang terjadi di pasar saat ini.

Mungkin sekarang Anda akan berteriak, “Jadi yang mana yang harus saya pakai? SMA atau EMA?” Hehe… jangan bingung ya. EMA maupun SMA memiliki kekurangan dan kelebihan tersendiri. Kita bahas satu per satu.

Kalau Anda adalah trader yang agresif dan ingin menggunakan MA yang bereaksi cepat terhadap pergerakan harga, maka EMA merupakan pilihan yang tepat. EMA bisa membantu Anda menangkap peluang lebih cepat dibandingkan SMA. Dengan demikian profit yang bisa Anda dapatkan tentunya akan lebih besar pula. Namun kekurangannya adalah Anda bisa saja terjebak oleh fake signal (sinyal palsu) yang diberikan oleh EMA.

Nah, SMA sendiri adalah kebalikan dari EMA. SMA bereaksi lebih lamban pada pergerakan harga daripada EMA. Dengan demikian, peluang yang diberikan pun akan lebih lambat muncul. Artinya, profit yang dihasilkan pun akan lebih kecil. Namun kemungkinan terjebak oleh fake signal lebih kecil.

Jadi pilih yang mana? Terserah Anda. Ya, benar-benar terserah Anda. Anda sudah tahu kekurangan dan kelebihan masing-masing MA. Pilih yang sesuai dengan karakter Anda.

Ingat selalu kalimat ini:

“JIKA HARGA SECARA UMUM BERGERAK DI ATAS MA, MAKA TREN YANG BERLANGSUNG ADALAH UPTREND. SEBALIKNYA JIKA HARGA SECARA UMUM BERGERAK DI BAWAH MA, MAKA TREN YANG BERLANGSUNG ADALAH DOWNTREND.”

Mudah kan? Inilah prinsip dasar penggunaan MA. Dengan demikian, berhati-hatilah jika harga bergerak menembus MA (terjadi breakout), karena hal tersebut merupakan indikasi awal (bukan kepastian) bahwa tren akan berubah arah .

Ingat juga bahwa pada saat uptrend strategi yang terbaik adalah Buy. Sebaliknya, pada saat downtrend strategi yang terbaik adalah Sell.

Pada saat uptrend, MA bisa Anda pergunakan sebagai area referensi untuk buy. Sebaliknya, pada saat downtrend, MA bisa Anda pergunakan sebagai area referensi untuk melakukan sell. Strategi yang biasanya diterapkan adalah bounce trading.

Mari kita cermati gambar berikut ini:

Dalam gambar di atas terlihat indikator SMA 50 yang diplot pada grafik 1 jam-an. Terlihat bahwa harga terkoreksi dan mendekati SMA 50 dan memantul. Dengan demikian Anda memperoleh konfirmasi bahwa terjadi pantulan. Level stop loss yang terlihat di gambar adalah exit point berdasarkan support yang terdekat. Level target yang diambil adalah resistance yang terdekat. Perlu diingat bahwa jika Anda akan melakukan buy menggunakan MA, maka pastikan bahwa garis MA sedang menanjak (naik).

Kita lihat apa yang terjadi kemudian.

Ternyata bounce yang terjadi valid dan target Anda tercapai.

Pada strategi sell, yang dilakukan sebenarnya hanya kebalikan dari strategi buy. Ketika harga mengalami pullback ke area MA, yang Anda lakukan adalah menunggu konfirmasi bounce untuk melakukan sell. Perhatikan gambar di bawah ini.

Contoh di atas juga mempergunakan SMA 50. Yang pertama kali harus Anda perhatikan adalah apakah garis SMA tersebut sedang turun. Ketika harga mengalami pullback ke area SMA, pastikan bahwa kemiringannya SMA tetap ke bawah (turun). Dalam gambar di atas, kita melihat bahwa harga persis menyentuh garis SMA. Memang ada false break, namun segera harga bergerak turun dan bergerak di bawah SMA. Keadaan ini menggambarkan bahwa tekanan bearish lebih besar daripada bullish. Pada saat ini Anda boleh langsung mengambil posisi sell dengan target di support terdekat dan stop loss di resistance terdekat.

Apa yang terjadi selanjutnya?

Ya… ya… sederhana memang, tapi ingat: tidak selamanya skenarionya seperti ini. Terkadang bounce yang terjadi gagal dan harga malah berbalik dan menembus MA dengan sadisnya. Itulah sebabnya Anda perlu menempatkan stop loss . Nantinya, dengan strategi ditambah manajemen resiko yang baik (akan dipelajari nanti pada level yang lebih tinggi), strategi yang sederhana pun bisa menghasilkan profit yang konsisten.

Nah, ada pengembangan dari penggunaan MA sebagai entry point. Salah satu pengembangan yang populer adalah mengkombinasikan dua buah MA di dalam satu grafik. Kombinasi yang cukup populer adalah kombinasi SMA 20 dan SMA 50. Strategi ini kita sebut sebagai “double MA” .

Idenya adalah memanfaatkan celah yang merupakan area di antara dua MA (apakah nanti Anda akan menggunakan SMA ataupun SMA, sama saja. Hanya saja dalam contoh ini kami menggunakan SMA). Dari gambar di atas Anda bisa melihat bahwa sell dilakukan ketika harga masuk ke dalam area yang dimaksud.

Kalau Anda akan melakukan transaksi dengan strategi double MA maka minimal dua kondisi berikut harus terpenuhi:

Kedua MA harus memiliki arah kemiringan yang sama. Jika akan BUY, maka kemiringan kedua MA harus ke atas (naik). Sebaliknya, jika akan SELL, maka kemiringan kedua MA harus ke bawah (turun).

Harga sudah berada di dalam celah yang merupakan area di antara dua MA.

Contoh di bawah ini adalah menggunakan strategi double MA untuk melakukan Buy.

Oke, Anda sudah tahu bahwa celah MA tersebut bisa Anda manfaatkan untuk entry. Pertanyaannya kemudian adalah: kapan persisnya Anda bisa buy atau sell?

Untuk sementara, Anda gunakan saja dulu area tersebut. Jadi ketika harga masuk dan candlestick ditutup di area tersebut, maka pada saat itulah Anda melakukan transaksi. Nantinya, akan ada alat bantu tambahan yang bisa membantu Anda untuk menentukan timing kapan harus melakukan aksi. Itu akan dipelajari di tingkat yang lebih lanjut. Stay tune!

Double MA Crossover

Perpotongan antara dua MA bisa Anda jadikan sinyal atau indikasi awal bahwa tren akan berubah arah. Hal tersebut juga bisa Anda pergunakan sebagai sinyal untuk entry .

Gambar di atas memperlihatkan SMA yang diplot di grafik 1 jam-an untuk currency pair GBP/USD. Pergerakan dari tanggal 27 Mei 2011 hingga lebih kurang 31 Mei 2011 adalah naik. Sekitar tanggal 1 Juni 2011, terjadi crossover (perpotongan) antara SMA 20 dan SMA 50. Setelah terjadi pullback sedikit, terlihat GBP/USD meluncur turun mulai tanggal 1 Juni 2011 hingga 2 Juni 2011.

Jika Anda melakukan sell ketika kedua SMA itu berpotongan, maka pada tanggal 2 Juni Anda sudah memperoleh setidaknya 100 pips. Yummy!

Kalau buy bagaimana? Sederhana saja, perpotongan dari bawah ke atas merupakan sinyalnya.

Perpotongan dua MA tersebut juga bisa Anda manfaatkan sebagai exit point jika Anda seandainya telah melakukan Buy berdasarkan strategi double MA sebelumnya. Jadi, selain sebagai entry point, perpotongan dua MA juga bisa digunakan sebagai exit point.

AR/MA, ARMA Acf - Pacf Visualizations

As mentioned in previous post. I have been working with Autoregressive and Moving Average simulations. To test the correctness of estimations by our simulations, we employ acf (Autocorrelation) and pacf (partial autocorrelation) to our use. For different order of AR and MA, we get the varying visualizations with them, such as:

Exponential decreasing curves.

Damped sine waves.

Positive and negative spikes, etc.

While analyzing and writing tests for same, I also took some time to visualize that data on ilne and bar charts to get a clearer picture:

AR(1) process

AR(1) process is the autoregressive simulation with order p = 1, i. e, with one value of phi. Ideal AR(p) process is represented by: To simulate this, install statsample-timeseries from here.

ACF

For AR(p), acf must give a damping sine wave. The pattern is greatly dependent on the value and sign of phi parameters. When positive content in phi coefficients is more, you will get a sine wave starting from positive side, else, sine wave will start from negative side. Notice, the damping sine wave starting from positive side here: and negative side here.

PACF

pacf gives spike at lag 0(value = 1.0, default) and from lag 1 to lag k. The example above, features AR(2) process, for this, we must get spikes at lag 1 - 2 as:

MA(1) process

MA(1) process is the moving average simulation with order q = 1. i. e, with one value of theta . To simulate this, use ma_sim method from Statsample::ARIMA::ARIMA

MA(q) process

ACF

PACF

ARMA(p, q) process

ARMA(p, q) is combination of autoregressive and moving average simulations. When q = 0. the process is called as pure autoregressive process; when p = 0. the process is purely moving average. The simulator of ARMA can be found as arma_sim in Statsample::ARIMA::ARIMA. For ARMA(1, 1) process, here are the comparisons of the visualizations from R and this code, which just made my day :)

Cheers, - Ankur Goel

Posted by Ankur Goel Jul 20 th. 2013

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I’ve always been a firm believer that moving averages probably give a better insight into trends within a business than a simple trend line associated to a set of values such as monthly sales (although I tend to review these two values together). The reason for this is that a trend can be skewed by one or two values that may not be representative of the underlying business such as spikes associated to seasonality or a specific event. When BillD highlighted a query regarding this concept in his comments on Profit & Loss (Part 2) – Compare and Analyse . I thought it would be a great idea to flex our P&L dataset to provide some Moving Average capability.

In this post, I will explain what moving averages are intended to deliver and explain how to calculate them using the sales elements of the example data used in the Profit & Loss series of posts. I will then add the flexibility for users to select the time frame that the moving average calculation should consider, the number of trend periods to be displayed and the end date of the report.

What is a Moving Average?

The most common moving average measure is generally referred to as a 12 month moving average. In the case of our sales data, for any given period, this measure would sum the last 12 months of sales preceding and including the month being analysed and then divide by 12 to show an average sales value for that timeframe. In financial terms, the equation is therefore quite simply:

12 Month Moving Average = Sum of Sales for Last 12 Months / 12

This all seems very straight forward but there’s a lot of complexity involved if we want to put the Moving Average timeframe (represented as 12 in the above example) in the hands of the user, give them the power to select the number of trend periods to be displayed and the month that the report should display up to.

The Dataset

The dataset that we’re using looks something like below.

Note – I’m using PowerPivot V1. Design viewer is available in V2 but I’ve hashed this together – nothing clever!

You’ll notice that FACT_Tran (our dataset to be analysed) is linked to DIM_Heading1, DIM_Heading2 and DIM_DataType to provide some categorisation to our dataset. I’ve also linked to Dates which is a sequential set of dates that more than covers the timespan of our dataset. This table carries some static additional information based on the date:

Once again, we’re not quite registering on Rob’s spicy scale! Rest assured that you’ll be getting a more intense DAX workout as we go on.

As these date measures aren’t expected to be dynamic, I’ve coded them in the PowerPivot window. This allows them to be calculated on file refresh but they won’t need to recalculate for each slicer operation which removes performance overhead from our ultimate dynamic measure.

For reasons that I’ll come on to later, I also need the month end date on my fact table as I can’t use the Month End Date on my Dates table in my measures. I can however pull the same value across to my FACT_Tran table using the following measure:

So What Are These Unlinked MA_ Tables?

The reason for these tables should become apparent as we go on. In brief, they’re going to be used as parameters or headings on our report. The reason that they exist and that they’re not linked to the rest of our data is simply because I don’t want them to be filtered by our measures. Instead, I want them to drive the filtering.

Initial PivotTable Setup

I’m going to be displaying a series of data organised in monthly columns. The user will be given slicers to set Month End Date (the last period to be shown on the report), Number of Periods for Moving Average (this will ultimately be part of our divisor calculation) and Number of Periods for Trend (this will be the number of monthly columns that we will display on our trend). We can establish these slicers straight away and link them to the pivot.

I obviously need a month end date as a column heading but which one? To some extent I’ve given this away earlier on. In short, I need to use my MA_Dates[Month_End_Date] field. The reason is that this field isn’t linked to our dataset and therefore won’t be affected by any other filters. If I use a date field that is part of my dataset or part of a linked table, the values available may be filtered down by the users selections. I can get around this using an ALL() expression to give me the correct values, but the problem is that the column is still filtered and my results will all be displayed in one column. It’s difficult to explain until you see it so please go ahead and try – it’s worth hitting the brick wall to really understand it !

Calculating Sum of Sales for Last X Months

The first part of our equation is to calculate the total value for sales across all periods within a dynamic timeframe to be selected by the user. For this I use a Calculate function that looks like this:

I’m using a base measure called Cascade_Value_All that was created in Profit & Loss – The Art of the Cascading Subtotal . I’m then filtering that measure to limit my dataset to records that relate to Sales and a data type of Actual (ie eliminating Budget). This is simple filtering of a CALCULATE function. However, it gets a bit more tasty with the third filter which limits the dataset to a series of dates that are dependent on the users selections in slicers and our date column heading.

The DATESBETWEEN function has the syntax DATESBETWEEN(dates, start_date, end_date) and works like this:

I set the field that requires filtering (Dates[Data]). I’ve found that this works best if this is a linked table of sequential dates without any breaks. If you have any breaks, there’s a chance you might not get an answer as the answer that you evaluate to has to be available in the table.

My start date is a DATEADD function that calculates the column heading date less the number of months that the user has selected on the “Moving Average No of Periods” slicer. I use the LASTDATE(VALUES(MA_Dates[Next_Month_Start_Date)) function to retrieve the Next_Month_Start_Date value from the MA_Dates table that relates to the date represented on the column heading. I then rewind by the number of months selected on the slicer using MAX(MA_Function_Periods[Moving_Average_No_Periods])*-1. The “-1” is used to go back in time. The reason I use Next_Month_Start_Date and a multiple of –1 is more clearly explained in Slicers For Selecting Last “X” Periods .

My end date is simply the Month_End_Date as shown on the column heading of the report. This is calculated using LASTDATE(VALUES(MA_Dates[Month_End_Date]).

That’s great, but my measure isn’t taking any account of my “Show Periods Up To” selection and the “Trend No of Periods” that I’ve selected. We therefore need to limit the measure to only execute when certain parameters hold as true based on these selections. I only want values to be displayed when my column heading date is:

Less than or equal to the selected Month End Date on my “Show Periods Up To” slicer AND

Greater than or equal to the selected Month End Date LESS the selected number of periods on my “Trend No of Periods” slicer.

To do this, I use an IF statement to determine when my CALCULATE function should execute. Let’s call this measure Sales_Moving_Average_Total_Value

The IF statement works as follows:

I first need to determine that I’m evaluating only where I have one value for MA_Date[Month_End_Date]. If I don’t do this, I get that old favourite error in my subsequent evaluation that says that a table of multiple values was supplied……

I then evaluate to determine if my column heading date (VALUES(MA_Dates[Month_End_Date]) is less than or equal to the date selected on the Month End Period slicer (LASTDATE(dates[Date_Month_End])… AND (&&)

My column heading date is greater than or equal to a calculated date which is X periods prior to the selected “Show Periods Up To” as selected on the Slicer. I use a DATEADD function for this similar to that used in my CALCULATE function except we’re adjusting the date by the value selected on the “Trend No of Periods” slicer.

With this in place, we have the total sales for the selected period relating to the users selections.

So my table is now limited to the number of trend periods selected and represents the month end date selected.

So Now We Just Divide By “Moving Average No of Periods” Right? eh NO!

We’ve calculated our total sales for the period relating to the users selections. You would be forgiven for suggesting that we simply divide by the number of moving average periods selected. Depending on your data, you could do this but the problem is that the dataset may not hold the selected number of periods, especially if the user can select a month end date that goes back in time. As a result, we need to work out how may periods are present in our Sales_Moving_Average_Total_Value measure.

This measure is essentially the same as my Sales_Moving_Average_Total measure. The only real difference is that we count the distinct date values in our dataset as opposed to calling the Cascade_Value_All measure. I mentioned earlier that there was a reason why I needed the month end date to be held on my FACT_Tran table and this is why. If I use any other table holding the month end date, that table isn’t going to have been filtered in the way that the core dataset has been filtered. As an example, my Dates table has a series of dates that spans my dataset timeframe and more. As a result, evaluating against this table will deduce that the table does in fact have dates that precede my dataset and there is therefore no evaluation as to whether there is a transaction held in the dataset for that date.

As you can see, since my dataset runs from 1st July 2009, I only have 9 periods of data to evaluate for my 31/03/2010 column. If I had divided by 12 (as per my “Moving Average No of Periods” slicer selection), I would have got a very wrong answer. Obviously, this is slightly contrived but it’s worthy of consideration.

And Now The Simple Bit

I can understand that the last two measures have taken some absorbing, especially working out when particular date fields should be used. For some light relief, the next measure won’t really tax you!

This is a simple division with a bit of error checking to avoid any nasties.

When It’s All Put Together

Since all of these measure are portable, I can create another Pivot Table on the same basis as the one above (with Sales_Moving_Average_Value given an alias of Moving Average), move some stuff around, add a measure for the actual sales value for the month (I won’t go into that now, but it’s a simple CALCULATE measure with some time intelligence) and I then reconfigure to look like the following:

I can then drive a simple line chart and apply a trend line to my “Actual” measure with the chart conveniently hiding my data grid that drives it.

As you can see, a trend on my Actual measure shows a steady decline. My Moving Average, however, shows a relatively stable, if not slightly improving trend. Seasonality of some other spikes are obviously therefore involved and the reality is that both measures probably need to be reviewed side by side.

For those of you reading this who are interested in seeing the workbook of this example, I’ll look to post this in a future post when I take this analysis one step further to cover the whole P&L. Sorry to make you wait.

I hope this helps you out BillD…

One More Point to Note

Those eagle eyed DAX pros out there have probably noticed that my IF functions only contain a calculation to evaluate when the logical test reaches a True answer. The reason is that the function assumes BLANK() when a false evaluation condition isn’t provided. I haven’t worked out if there’s any performance impact using this method on large datasets. It’s up to you what you chose to do and if anyone can convince me why coding the False condition as BLANK() is best practice, I will quickly change my habits!

Por favor, comparta esto

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What Is the DIG Hull Moving Average?

The DIG Hull Moving Average ― the HMA ― makes your moving average responsive to current prices while remaining smooth and not choppy. La belleza de la HMA es que logra eliminar el retraso casi completamente mientras se mantiene perfectamente liso.

This is what you are looking for in a moving average; it means that you can get your signals faster and make fewer mistakes.

How Does the HMA Compare to Other Moving Averages?

Let’s start by comparing the HMA to a simple moving average (SMA) of the same length. Just a quick reminder: The SMA calculation takes the past “n” closing prices and calculates their average; usually it is traded by taking a short and long SMA and when the two cross a signal occurs. The SMA is associated with two problematic issues:

Longer length -> Lag becomes significantly bigger.

Sort length -> The MA becomes very choppy

S&P500 Futures Daily Chart: On the chart you can see the standard SMA (length 34) in cyan/light blue, and our _DIG__Hull_Moving_Average (length 34) in yellow. El lado izquierdo del gráfico muestra que mientras el SMA sigue subiendo contra el mercado, el HMA está atrapando ambos pivotes y cambiando de dirección mientras permanece liso.

You can also see how big the delay/lag actually is by looking at the two vertical lines on the right; the SMA changes its direction about 15 bars later than our HMA – this means that you would have gotten into the trade earlier and enjoyed that nice bearish move.

Now let’s add the standard exponential moving average (EMA). The main idea behind the EMA is to provide more significance to the newer data there for eliminating lag; you will notice that the HMA is actually even better than the EMA as it will react faster but remain smooth.

S&P500 Futures Daily Chart: SMA (length 34) in cyan/light blue. EMA (longitud 34) en púrpura. _DIG__Hull_Moving_Average (length 34) in yellow.

Usted puede ver que el EMA está entre el HMA y el SMA. Es más sensible que el SMA, pero una milla detrás de la HMA. También puede ver que la línea EMA no es tan suave como la línea HMA.

Para resumir, el EMA es una mejora de la SMA, y nuestro DIG Hull Moving Average lleva esto aún más lejos, proporcionando una media móvil más suave y más precisa de lo que nunca has visto antes.

MA Trend Feature: Hemos añadido otra característica que hace que este indicador sea aún mejor. Usando un simple interruptor, puede decirle a nuestro indicador DIG HMA que se coloree según su dirección.

Let’s see it in action: AAPL 30 Min Chart: The DIG HMA is color coded according to its direction, making it much easier to get signals quickly. We have placed two DIG HMA indicators, one with the length of 34 and one with the length of 80; you can see three great cross signals.

Low lag -> Get in before other traders.

Supper smooth moving average -> Eliminate false entries.

New Feature – Color coded according to trend.

Fácil de usar y soporta cualquier gráfico y cualquier período de tiempo.

Download DIG Hull Moving Average For Free!

Dear Sir, I just read article about McGinley Dynamics http://www. mta. org/eweb/dynamicpage. aspx? webcode=journal-technical-analy. . Donde John R. McGinley argumenta que su indicador tiene una ventaja contra los promedios móviles. However, article was written in 1997 and Mr. McGinley states that it is impossible to program his indicator. I want to know more about this indicator and did research on web but unfortunately can't find anything else and up to date. Do you familiar with this indicator and is it better than MA?

I've made a copy for further reference. ¡Gracias! Yet, I haven't seen this exact report before to comment, sorry. But I can tell one thing - it's possible to code anything this days. I've seen sophisticated programmers who even manage to build & code indicators with artificial intelligence. how they work I don't know, but the possibilities of indicator/EA coding has moved far beyond a simple challenge of coding a Moving Average - these are hundreds of custos MAs with smoothing, shifting other adjustments etc. The best know forum for finding MT4 indicators is forex-tsd. com

Well done, thanks for the good work, please, what would your suggest to be recommended setting for 4hours time frame. Gracias una vez más

Cuando leo acerca de los períodos para la MA o cualquier indicador, los períodos se expresan en días, por ejemplo. 10-day period, 200-day period, 40-day period, etc. But is this actually the case? Are the periods actually an average of days or are they actually an average of bars in a timeframe? In other words, if I'm using a H1 timeframe and have the MA set to 24 periods, are these periods actually an averaging of the past 24 days or are they actually an averaging of the past 24 hours?

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thanks alot for explanation it's wonderful. but wat are the best settings for MA when trading?

Hello "Allows you to enter two ema periods and it will then show you at | | Which point they crossed over. It is more usful on the shorter | | periods that get obscured by the bars / candlesticks and when | | the zoom level is out. Also allows you then to remove the emas | | from the chart. (emas are initially set at 5 and 6)". This is for two EMAS crossover I would like the codo for thee EMAS 10 EMA, 25EMA and 50EMA cross over is it available and how to implement it? Saludos

hi, very useful info, but I would like to know what parameters to input for the EMA for the 30M time frame. Gracias

Pls can anyone tell me how to use the MA in MT4 15 Mins?

The most profound and yet the most silmpe comment on Support/Resistance was made by Mark McConnell: All trends start or stop at support or resistance. All we have to do as traders is figure out whether the Support/Resistance is acting like a trampoline or a breakable thin layer of ice.

Hola. i currently testing 2 moving averages together that is 5 (exponential) and 15 (simple) for scalping, question :-

1. what is the best time frame to be used for buy and sell signal?

2. what is the best additional indicator to support this method?

appreciate that you could help me out on this formula, many thanks..

Exponential Moving Average (EMA)

To measure an exponential moving average . unite a definite percentage of the actual value with an inverse percentage of the latter value of the exponential moving average .

If you have given 25% weight to the actual value, you should sum up 25% of the actual value to 75% of the previous moving average to get the actual moving average.

To define the corresponding weight which previous values should be given, use the period.

To determine the percentage, use the formula:

A period of 7 will result in 25% (2/ (7+1)) of the actual value and you use 75% of the previous exponential moving average value).

Caution: All previous values (including values prior to the period) form an actual exponential moving average. The period is used as an approximate calculation of the time period for which values will stay essential in the estimation. At the start of a data series, the value is supposed to be zero so you may pay more attention to the values until the period is finished.

Moving Averages may turn out to be helpful for smoothing raw, noisy data, for example, daily prices. Price data can change very much from every day and still conceal if the price is growing or decreasing. You see even a more general picture of the basic trends can if you watch the moving price average.

Occasionally, moving averages are applied for defining the trend, but they can also be used to see whether data is opposing the trend. Entry and exit systems usually compare data to a moving average to determine if it is supporting a trend or starting a new one. That is why the exponential moving average is just one of the types of a moving average.

In an ordinary moving average, all price data has the same weight in the calculation of the average with the oldest eliminated value as each new value is added. In the exponential moving average equation, while the average is being measured, the most recent market action gets greater importance. Still the oldest pricing data in the exponential moving average is never eliminated.

A sell signal occurs if the short and intermediate term averages cross from the top to the bottom the longer-term average. On the contrary, a purchase signal happens if the short and intermediate term averages cross from bottom over the longer-term average. If you trade only 2 exponential moving averages in a crossover system, it is better to use longer-term averages.

It is rather important to know that a 5-day exponential moving average usually consists of over 5 days worth of data and can comprise data from all the life of a futures contract. So such moving averages can be more successfully searched by their actual "smoothing constants," as the number of days of data in the computation remains equal for the 5-day average as for the 10-day average. Exponential calculations are held at various moving average values depending on the point you start with.

Autoregressive Moving Average Error Processes

& # 13; & # 13; & # 13; & # 13; & # 13; & # 13; Autoregressive moving average error processes (ARMA errors) and other models involving lags of error terms can be estimated using FIT statements and simulated or forecast using SOLVE statements. ARMA models for the error process are often used for models with autocorrelated residuals. The %AR macro can be used to specify models with autoregressive error processes. The %MA macro can be used to specify models with moving average error processes.

Autoregressive Errors

A model with first-order autoregressive errors, AR(1), has the form

while an AR(2) error process has the form

and so forth for higher-order processes. Note that the 's are independent and identically distributed and have an expected value of 0.

An example of a model with an AR(2) component is You would write this model as follows:

or equivalently using the %AR macro as

Moving Average Models

& # 13; A model with first-order moving average errors, MA(1), has the form

where is identically and independently distributed with mean zero. An MA(2) error process has the form

and so forth for higher-order processes.

For example, you can write a simple linear regression model with MA(2) moving average errors as

where MA1 and MA2 are the moving average parameters.

Note that RESID. Y is automatically defined by PROC MODEL as Note that RESID. Y is .

The ZLAG function must be used for MA models to truncate the recursion of the lags. This ensures that the lagged errors start at zero in the lag-priming phase and do not propagate missing values when lag-priming period variables are missing, and ensures that the future errors are zero rather than missing during simulation or forecasting. For details on the lag functions, see the section "Lag Logic."

This model written using the %MA macro is

General Form for ARMA Models

The general ARMA( p, q ) process has the following form

An ARMA( p , q ) model can be specified as follows

where AR i and MA j represent the autoregressive and moving average parameters for the various lags. You can use any names you want for these variables, and there are many equivalent ways that the specification could be written.

Vector ARMA processes can also be estimated with PROC MODEL. For example, a two-variable AR(1) process for the errors of the two endogenous variables Y1 and Y2 can be specified as follows

Convergence Problems with ARMA Models

ARMA models can be difficult to estimate. If the parameter estimates are not within the appropriate range, a moving average model's residual terms will grow exponentially. The calculated residuals for later observations can be very large or can overflow. This can happen either because improper starting values were used or because the iterations moved away from reasonable values.

Care should be used in choosing starting values for ARMA parameters. Starting values of .001 for ARMA parameters usually work if the model fits the data well and the problem is well-conditioned. Note that an MA model can often be approximated by a high order AR model, and vice versa. This may result in high collinearity in mixed ARMA models, which in turn can cause serious ill-conditioning in the calculations and instability of the parameter estimates.

If you have convergence problems while estimating a model with ARMA error processes, try to estimate in steps. First, use a FIT statement to estimate only the structural parameters with the ARMA parameters held to zero (or to reasonable prior estimates if available). Next, use another FIT statement to estimate the ARMA parameters only, using the structural parameter values from the first run. Since the values of the structural parameters are likely to be close to their final estimates, the ARMA parameter estimates may now converge. Finally, use another FIT statement to produce simultaneous estimates of all the parameters. Since the initial values of the parameters are now likely to be quite close to their final joint estimates, the estimates should converge quickly if the model is appropriate for the data.

AR Initial Conditions

& # 13; & # 13; & # 13; & # 13; & # 13; & # 13; & # 13; & # 13; & # 13; & # 13; The initial lags of the error terms of AR( p ) models can be modeled in different ways. The autoregressive error startup methods supported by SAS/ETS procedures are the following:

CLS conditional least squares (ARIMA and MODEL procedures)

ULS unconditional least squares (AUTOREG, ARIMA, and MODEL procedures)

ML maximum likelihood (AUTOREG, ARIMA, and MODEL procedures)

YW Yule-Walker (AUTOREG procedure only)

HL Hildreth-Lu, which deletes the first p observations (MODEL procedure only) See Chapter 8. for an explanation and discussion of the merits of various AR(p) startup methods.

The CLS, ULS, ML, and HL initializations can be performed by PROC MODEL. For AR(1) errors, these initializations can be produced as shown in Table 14.2. These methods are equivalent in large samples.

Table 14.2: Initializations Performed by PROC MODEL: AR(1) ERRORS

MA Initial Conditions

& # 13; & # 13; & # 13; & # 13; & # 13; & # 13; The initial lags of the error terms of MA( q ) models can also be modeled in different ways. The following moving average error startup paradigms are supported by the ARIMA and MODEL procedures:

ULS unconditional least squares

CLS conditional least squares

ML maximum likelihood The conditional least-squares method of estimating moving average error terms is not optimal because it ignores the startup problem. This reduces the efficiency of the estimates, although they remain unbiased. The initial lagged residuals, extending before the start of the data, are assumed to be 0, their unconditional expected value. This introduces a difference between these residuals and the generalized least-squares residuals for the moving average covariance, which, unlike the autoregressive model, persists through the data set. Usually this difference converges quickly to 0, but for nearly noninvertible moving average processes the convergence is quite slow. To minimize this problem, you should have plenty of data, and the moving average parameter estimates should be well within the invertible range.

This problem can be corrected at the expense of writing a more complex program. Unconditional least-squares estimates for the MA(1) process can be produced by specifying the model as follows:

Moving-average errors can be difficult to estimate. You should consider using an AR( p ) approximation to the moving average process. A moving average process can usually be well-approximated by an autoregressive process if the data have not been smoothed or differenced.

The %AR Macro

The SAS macro %AR generates programming statements for PROC MODEL for autoregressive models. The %AR macro is part of SAS/ETS software and no special options need to be set to use the macro. The autoregressive process can be applied to the structural equation errors or to the endogenous series themselves.

The %AR macro can be used for

univariate autoregression

unrestricted vector autoregression

restricted vector autoregression.

Univariate Autoregression

& # 13; To model the error term of an equation as an autoregressive process, use the following statement after the equation:

For example, suppose that Y is a linear function of X1 and X2, and an AR(2) error. You would write this model as follows:

The calls to %AR must come after all of the equations that the process applies to.

The proceding macro invocation, %AR(y,2), produces the statements shown in the LIST output in Figure 14.49.

Figure 14.50: LIST Option Output for an AR Model with Lags at 1, 12, and 13

There are variations on the conditional least-squares method, depending on whether observations at the start of the series are used to "warm up" the AR process. By default, the %AR conditional least-squares method uses all the observations and assumes zeros for the initial lags of autoregressive terms. By using the M= option, you can request that %AR use the unconditional least-squares (ULS) or maximum-likelihood (ML) method instead. Por ejemplo:

Discussions of these methods is provided in the "AR Initial Conditions" earlier in this section.

By using the M=CLS n option, you can request that the first n observations be used to compute estimates of the initial autoregressive lags. In this case, the analysis starts with observation n +1. Por ejemplo:

You can use the %AR macro to apply an autoregressive model to the endogenous variable, instead of to the error term, by using the TYPE=V option. For example, if you want to add the five past lags of Y to the equation in the previous example, you could use %AR to generate the parameters and lags using the following statements:

The preceding statements generate the output shown in Figure 14.51.

The MODEL Procedure

Listing of Compiled Program Code

Statement as Parsed

PRED. y = a + b * x1 + c * x2;

RESID. y = PRED. y - ACTUAL. y;

ERROR. y = PRED. y - y;

#OLD_PRED. y = PRED. y + y_l1 * ZLAG1( y ) + y_l2 * ZLAG2( y ) + y_l3 * ZLAG3( y ) + y_l4 * ZLAG4( y ) + y_l5 * ZLAG5( y );

RESID. y = PRED. y - ACTUAL. y;

ERROR. y = PRED. y - y;

Figure 14.51: LIST Option Output for an AR model of Y

This model predicts Y as a linear combination of X1, X2, an intercept, and the values of Y in the most recent five periods.

Unrestricted Vector Autoregression

& # 13; To model the error terms of a set of equations as a vector autoregressive process, use the following form of the %AR macro after the equations:

The process_name value is any name that you supply for %AR to use in making names for the autoregressive parameters. You can use the %AR macro to model several different AR processes for different sets of equations by using different process names for each set. The process name ensures that the variable names used are unique. Use a short process_name value for the process if parameter estimates are to be written to an output data set. The %AR macro tries to construct parameter names less than or equal to eight characters, but this is limited by the length of name . which is used as a prefix for the AR parameter names.

The variable_list value is the list of endogenous variables for the equations.

For example, suppose that errors for equations Y1, Y2, and Y3 are generated by a second-order vector autoregressive process. You can use the following statements:

which generates the following for Y1 and similar code for Y2 and Y3:

Only the conditional least-squares (M=CLS or M=CLS n ) method can be used for vector processes.

You can also use the same form with restrictions that the coefficient matrix be 0 at selected lags. For example, the statements

apply a third-order vector process to the equation errors with all the coefficients at lag 2 restricted to 0 and with the coefficients at lags 1 and 3 unrestricted.

You can model the three series Y1-Y3 as a vector autoregressive process in the variables instead of in the errors by using the TYPE=V option. If you want to model Y1-Y3 as a function of past values of Y1-Y3 and some exogenous variables or constants, you can use %AR to generate the statements for the lag terms. Write an equation for each variable for the nonautoregressive part of the model, and then call %AR with the TYPE=V option. Por ejemplo,

The nonautoregressive part of the model can be a function of exogenous variables, or it may be intercept parameters. If there are no exogenous components to the vector autoregression model, including no intercepts, then assign zero to each of the variables. There must be an assignment to each of the variables before %AR is called.

This example models the vector Y=(Y1 Y2 Y3) ' as a linear function only of its value in the previous two periods and a white noise error vector. The model has 18=(3 × 3 + 3 × 3) parameters.

Syntax of the %AR Macro

There are two cases of the syntax of the %AR macro. The first has the general form

name specifies a prefix for %AR to use in constructing names of variables needed to define the AR process. If the endolist is not specified, the endogenous list defaults to name . which must be the name of the equation to which the AR error process is to be applied. The name value cannot exceed eight characters.

nlag is the order of the AR process.

endolist specifies the list of equations to which the AR process is to be applied. If more than one name is given, an unrestricted vector process is created with the structural residuals of all the equations included as regressors in each of the equations. If not specified, endolist defaults to name .

laglist specifies the list of lags at which the AR terms are to be added. The coefficients of the terms at lags not listed are set to 0. All of the listed lags must be less than or equal to nlag . and there must be no duplicates. If not specified, the laglist defaults to all lags 1 through nlag .

M= method specifies the estimation method to implement. Valid values of M= are CLS (conditional least-squares estimates), ULS (unconditional least-squares estimates), and ML (maximum-likelihood estimates). M=CLS is the default. Only M=CLS is allowed when more than one equation is specified. The ULS and ML methods are not supported for vector AR models by %AR.

TYPE=V specifies that the AR process is to be applied to the endogenous variables themselves instead of to the structural residuals of the equations.

Restricted Vector Autoregression

& # 13; & # 13; & # 13; & # 13; You can control which parameters are included in the process, restricting those parameters that you do not include to 0. First, use %AR with the DEFER option to declare the variable list and define the dimension of the process. Then, use additional %AR calls to generate terms for selected equations with selected variables at selected lags. Por ejemplo,

The error equations produced are

This model states that the errors for Y1 depend on the errors of both Y1 and Y2 (but not Y3) at both lags 1 and 2, and that the errors for Y2 and Y3 depend on the previous errors for all three variables, but only at lag 1.

%AR Macro Syntax for Restricted Vector AR

An alternative use of %AR is allowed to impose restrictions on a vector AR process by calling %AR several times to specify different AR terms and lags for different equations.

The first call has the general form

name specifies a prefix for %AR to use in constructing names of variables needed to define the vector AR process.

nlag specifies the order of the AR process.

endolist specifies the list of equations to which the AR process is to be applied.

DEFER specifies that %AR is not to generate the AR process but is to wait for further information specified in later %AR calls for the same name value. The subsequent calls have the general form

name is the same as in the first call.

eqlist specifies the list of equations to which the specifications in this %AR call are to be applied. Only names specified in the endolist value of the first call for the name value can appear in the list of equations in eqlist .

varlist specifies the list of equations whose lagged structural residuals are to be included as regressors in the equations in eqlist . Only names in the endolist of the first call for the name value can appear in varlist . If not specified, varlist defaults to endolist .

laglist specifies the list of lags at which the AR terms are to be added. The coefficients of the terms at lags not listed are set to 0. All of the listed lags must be less than or equal to the value of nlag . and there must be no duplicates. If not specified, laglist defaults to all lags 1 through nlag .

The %MA Macro

& # 13; The SAS macro %MA generates programming statements for PROC MODEL for moving average models. The %MA macro is part of SAS/ETS software and no special options are needed to use the macro. The moving average error process can be applied to the structural equation errors. The syntax of the %MA macro is the same as the %AR macro except there is no TYPE= argument.

& # 13; When you are using the %MA and %AR macros combined, the %MA macro must follow the %AR macro. The following SAS/IML statements produce an ARMA(1, (1 3)) error process and save it in the data set MADAT2.

The following PROC MODEL statements are used to estimate the parameters of this model using maximum likelihood error structure: The estimates of the parameters produced by this run are shown in Figure 14.52.

Maximum Likelihood ARMA(1, (1 3))

Figure 14.52: Estimates from an ARMA(1, (1 3)) Process

Syntax of the %MA Macro

There are two cases of the syntax for the %MA macro. The first has the general form

name specifies a prefix for %MA to use in constructing names of variables needed to define the MA process and is the default endolist .

nlag is the order of the MA process.

endolist specifies the equations to which the MA process is to be applied. If more than one name is given, CLS estimation is used for the vector process.

laglist specifies the lags at which the MA terms are to be added. All of the listed lags must be less than or equal to nlag . and there must be no duplicates. If not specified, the laglist defaults to all lags 1 through nlag .

%MA Macro Syntax for Restricted Vector Moving Average

& # 13; An alternative use of %MA is allowed to impose restrictions on a vector MA process by calling %MA several times to specify different MA terms and lags for different equations.

The first call has the general form

name specifies a prefix for %MA to use in constructing names of variables needed to define the vector MA process.

nlag specifies the order of the MA process.

endolist specifies the list of equations to which the MA process is to be applied.

DEFER specifies that %MA is not to generate the MA process but is to wait for further information specified in later %MA calls for the same name value. The subsequent calls have the general form

name is the same as in the first call.

eqlist specifies the list of equations to which the specifications in this %MA call are to be applied.

varlist specifies the list of equations whose lagged structural residuals are to be included as regressors in the equations in eqlist .

laglist specifies the list of lags at which the MA terms are to be added.

I can set Moving Average Levels on my charts in the dialog box settings,

so how do I program the MA Levels into an EA lines of code?

To Buy when Price is between the MA Level values of up +20 and +40.

To Sell when Price is between the MA Level values of down -20 and -40.

Standard Moving Average Parameters allow for shift to the right and left only.

As MetaTrader lets me set MA Levels on the charts, surely there must be a way to program MA Levels into an EA.

Can anyone help me solve this puzzle?

Use iMA () in your EA to get the moving average, then add/subtract from that to get the levels.

I am also looking for the source code for this. The built-in indicator cannot be modified in editor, and the source code posted online is for the Custom Indicator "Moving Averages" (which does not let you add levels), not the built-in "Moving Average" which lets you add "Levels".

If someone can post the code or knows where to find it, there would be more than one person that would appreciate this!

Why Every Trader Needs to Watch the 200-Day Moving Average

Moving averages (MA’s) are among the most popular tools available to portfolio managers, analysts, investors and traders but are they being used in the most effective way? We have stressed the importance of MA’s many times and this article will teach you how, and why, we use them.

The simple moving average (SMA) is the most common type of MA used. This method uses a fixed number of data points as the data series moves forward. For example, a 200-day SMA will average the most recent 200-days worth of data (usually closing prices). With each new day, a new data point is added and the oldest data point is removed. In other words, the 200-day SMA displays the arithmetic mean of the most recent 200-days of closing prices.

It is important to determine the right length MA for your intended purpose. We use the 200-day SMA as a trend filter for stocks and indices. A stock or index trading above the 200-day SMA is considered to be in an uptrend, while a stock or index trading below the 200-day SMA is considered to be in a downtrend. Our research shows that using the 200-day SMA in this manner improves the test results.

We have also published research that uses the 5-day SMA or 10-day SMA to take profits/exit trades. We use these shorter MA’s because our research shows them to be among the better exit strategies available.

Why the 200-day MA is so important

Here’s a look at how the S&P 500 and the NASDAQ 100 has performed in relation to the 200-day MA. The test period covers from 1/1/89 to 6/30/06. The tables below shows the average percentage gain/loss for SPX and NDX during our test period over a 1-day, 2-day, and 1-week (5-days) period.

Historically, the SPX outperforms when it is trading above the 200-day MA, 2-days and 1-week later.

Historically, the SPX underperforms when it is trading below the 200-day MA, 1-day, 2-days and 1-week later.

Historically, the NDX outperforms when it is trading above the 200-day MA, 1-day, 2-days and 1-week later.

Historically, the NDX underperforms when it is trading below the 200-day MA, 1-day, 2-days and 1-week later.

This research can be extended to cover stocks too. We looked at over seven million trades from 1/1/95 to 6/30/06*. The table below shows the average percentage gain/loss for all stocks during our test period over a 1-day, 2-day, and 1-week (5-days) period.

Historically, stocks slightly outperform the benchmark when trading above the 200-day MA, 2-days and 1-week later.

Historically, stocks underperform the benchmark when trading below the 200-day MA, 1-week later.

This information, combined with our days of the month study, PowerRatings. and the other research we have recently published (view archives ) shows how to build successful trading strategies.

How to use this information

When you go to the new TradingMarkets Stock Indicators page you’ll see that all of the indicators (bullish and bearish) use the 200-day MA. The bullish stocks are all trading above the 200-day MA, while the bearish ones are all trading below the 200-day MA. The lists are filtered this way because our research shows an even greater edge can be obtained.

Please send me any questions or comments you may have regarding this article.

David Penn is Editor-in-Chief of TradingMarkets. com.

Larry Connors is CEO and Founder of TradingMarkets. com, and Connors Research.

* Our research looked at 7,050,517 trades from Jan 1, 1995 to June 30, 2006. We applied a price and liquidity filter that required all stocks be priced above $5 and have a 100-day moving average of volume greater than 250,000 shares.

About Larry Connors

Larry Connors has over 30 years in the financial markets industry. His opinions have been featured at the Wall Street Journal, Bloomberg, Dow Jones, & many others. For over 15 years, Larry Connors and now Connors Research has provided the highest-quality, data-driven research on trading for individual investors, hedge funds, proprietary trading firms, and bank trading desks around the world.

Recent Articles on TradingMarkets

Moving Averages, MA

The Moving Average Technical Indicator shows the mean instrument price value for a certain period of time. Cuando se calcula la media móvil, se calcula la media del precio del instrumento para este período de tiempo. A medida que el precio cambia, su promedio móvil aumenta o disminuye. There are four different types of moving averages: Simple (also referred to as Arithmetic), Exponential, Smoothed and Linear Weighted. Los promedios móviles se pueden calcular para cualquier conjunto de datos secuenciales, incluyendo precios de apertura y cierre, precios más altos y más bajos, volumen de operaciones o cualquier otro indicador. A menudo es el caso cuando se usan promedios móviles dobles. Lo único en que los promedios móviles de diferentes tipos divergen considerablemente entre sí, es cuando los coeficientes de peso, que se asignan a los últimos datos, son diferentes. En caso de que se trate de media móvil simple, todos los precios del período de tiempo en cuestión, son iguales en valor. Exponential and Linear Weighted Moving Averages attach more value to the latest prices. La forma más común de interpretar el precio promedio móvil es comparar su dinámica con la acción del precio. When the instrument price rises above its moving average, a buy signal appears, if theprice falls below its moving average, what we have is a sell signal. Este sistema de comercio, que se basa en la media móvil, no está diseñado para proporcionar la entrada en el mercado justo en su punto más bajo, y su salida a la derecha en el pico. It allows to act according to the following trend. to buy soon after the prices reach the bottom, and to sell soon after the prices have reached their peak.

Cálculo

Simple Moving Average (SMA) Simple, in other words, arithmetical moving average is calculated by summing up the prices of instrument closure over a certain number of single periods (for instance, 12 hours). Este valor se divide entonces por el número de tales períodos.

SMA = SUM(CLOSE, N)/N

Where: N — is the number of calculation periods.

Exponential Moving Average (EMA) Exponentially smoothed moving average is calculated by adding the moving average of a certain share of the current closing price to the previous value. Con los promedios móviles suavizados exponencialmente, los últimos precios son de mayor valor. P-percent exponential moving average will look like:

Where: CLOSE(i) — the price of the current period closure; EMA(i-1) — Exponentially Moving Average of the previous period closure; P — the percentage of using the price value.

Smoothed Moving Average (SMMA) The first value of this smoothed moving average is calculated as the simple moving average (SMA):

SUM1 = SUM(CLOSE, N)

The second and succeeding moving averages are calculated according to this formula:

Where: SUM1 — is the total sum of closing prices for N periods; SMMA1 — is the smoothed moving average of the first bar; SMMA(i) — is the smoothed moving average of the current bar (except for the first one); CLOSE(i) — is the current closing price; N — is the smoothing period.

Linear Weighted Moving Average (LWMA) In the case of weighted moving average, the latest data is of more value than more early data. Weighted moving average is calculated by multiplying each one of the closing prices within the considered series, by a certain weight coefficient.

LWMA = SUM(Close(i)*i, N)/SUM(i, N)

Where: SUM(i, N) — is the total sum of weight coefficients.

Here are the types of moving averages on the chart:

Simple Moving Average (SMA)

Exponential Moving Average (EMA)

Smoothed Moving Average (SMMA)

Linear Weighted Moving Average (LWMA)

Technical Indicator Description

Why You Shouldn’t Use Moving Averages

OK, here it is: I hate moving averages. Well, maybe “hate” is a strong word. But what gets me is that they’re everywhere – and they’re NOT REALLY THAT GOOD.

When I hear commentators talk about “bouncing off the 50-day moving average” or the “200-day moving average is rising so the trend is up” & # 8211; I want to shout at my computer screen. It’s so arbitrary. Why 200-day? What if the 200-day moving average was rising but the 175-day was falling?

You think I’m kidding don’t you? No, I’m serious. I can’t stand moving averages. And here are another couple of reasons why:

Moving averages assume the market is either going up or down. They are either rising or falling. But the market isn’t that simple – there aren’t just 2 states. In fact there are 3 states: the market is either rising, falling or in congestion. A moving average can’t help you determine this third congestion phase.

There are literally millions of different moving averages. Simple, exponential, weighted, etc. etc. Then 9 bar, 13 bar, 21 bar, 50 bar, etc. etc. Add all those combinations together and you literally have an infinite number of combinations. And so which one is “right”?

There is an analytical technique to determine uptrends, downtrends and market congestion. It works for all markets, all timeframes. Yes, it’s a little more complex than a moving average calculation – but that’s the point. We now have the computer power and the digital signal processing techniques to do this. And yes, I’m talking about the Hilbert Transform and the Better Sine Wave indicator .

Increased computer power means we can do better than a moving average!

Click for video transcript …

It is Thanksgiving weekend, so if you celebrate Thanksgiving, hope you’re enjoying your holiday. And in this video, I want to talk about moving averages and why I think you should ditch them, which is a bit of a big fight to pick, because if there’s one thing I can guarantee, you’re probably using a moving average on your favorite chart setup.

If not a moving average then a MACD, which is the difference between two moving averages. So, going against the grain here, kind of against the conventional wisdom, but just give me a few minutes and I’ll try and explain my point.

And why are moving averages so 1956? What’s the significance of the year 1956? 1956 was the year Robert Brown and his co-creator Charles Holt published a book on the exponential moving average, so it’s the first time it came into the public consciousness. They’d been using the moving average for 8 or 10 years previously.

They both worked for the U. S. Navy, although independently, and originally the exponential moving average was used to track the location of submarines. Later, it was used for demand forecasting and inventory control.

The beauty of the exponential moving average is that you only need two numbers to make the calculation. So here’s the little formula for an exponential moving average: it is yesterday’s value of the exponential moving average, or the previous bar’s value, times some factor, alpha, plus (1 – alpha) times the latest piece of data, whether that’s today’s price or the last bar’s price.

So as a little example here: if alpha was 0.8, you multiply the current value of the exponential moving average, say 100, by 0.8 then add (1 – 0.8), which is 0.2, times the current piece of data that comes along, which might be 110. Add those two numbers together, you’ve got 102. Easy mental arithmetic to do.

If you’re using a 10 or a 25 period simple moving average, you’d have to add together 10 or 25 different numbers and then divide by 25 or 10 or whatever it might be. With an exponential moving average, you only needed two numbers. And then in the days before the first pocket calculators were available, this was a godsend. Beautiful.

So 1956 was an important year. Prior to that, technical analysis has been very graphically-based. It’s all about trend lines and support resistance lines and things that you could do on a chart. After 1956, it was far more computationally-based, where we’re actually calculating moving averages and we’re using computer power basically to generate technical analysis signals.

Now, the problem with this is this increased computer power we’ve had ever since then has led us down the wrong path, in my opinion. The search for the ultimate moving average that smoothes out periods of consolidation.

Here’s a 4,500 tick bar chart of the Emini continuous contract day and night session going back about 7 or 8 days, and I’ve just got a simple moving average here place over this. It doesn’t matter on the length of this particular moving average, but if it’s falling, it’s colored in white. If it’s rising, it’s colored in red.

And you can see the trending moves quite nicely marked. Downtrend going here, uptrend going here, and so on. But, in between that, we have these periods of consolidation, where the market is trying to determine which way it’s going to go. And our moving average is all over the place. You can see here, it’s colored red and white and going backwards and forwards. Another little bit of a trending move here: red and white going backwards and forwards and so on. And then through this consolidation phase, exactly the same thing.

During these periods of uncertainty or congestion, the moving average does not do very well at modeling. You don’t know whether the market’s going up or going down. A lot of false signals going on. So, all the activity that’s gone on in developing moving averages is all been about trying to find this ultimate moving average that smoothes out those periods of consolidation.

And the result is we literally have thousands of combinations of different moving averages. I’ve just, off the top of my head, listed some of the ones programmed in my EasyLanguage and TradeStation here. Obviously, we’ve got simple moving averages, exponential, weighted moving averages. We could also do medians of price values. There’s the T3, the TEMA, the Hull Moving Average. A quite nice little moving average. There’s the JMA, the Jurik Moving Average. Again, a very nice little moving average – very clever.

The whole of John Ehlers’ filters, and he’s done dozens and dozens of different filters, one of those is the Laguerre filter. Also the MAMA and FAMA moving averages. We’ve got linear regressions, zero lag filters, elliptics, and then multiple moving averages, and the difference between those multiple moving averages, and so on.

So, as you can see, there are dozens of different types of moving averages. Then, on top of that, you’ve got to choose the length, or the smoothing factor, for each of these to use. And then you could also be displacing these moving averages. So, put all of that together, and you’ve got a myriad of different choices of moving averages to use. And all they’re trying to do is smooth out these periods of consolidation and limit the number of false signals you get.

The problem that I have is that instead of trying to find this ultimate moving average, what we should be looking for is an indicator that tells us what kind of activity the market is going through. If the market is trending, a moving average will be fantastic at showing you signals in a trending market. But when a market is not trending, but is consolidating, the moving average will be horrible.

So you need an indicator that will tell you which kind of activity the market is going through at the moment, so that you can apply the right piece of analysis. In effect, what you’re calculating is the support and resistance levels adaptively. Because once you break out of a support or resistance level, that’s when you move into a trending period. John Ehlers to the rescue.

Beautiful piece of code he developed called the Hilbert Sine Wave, which I’ve improved on, called the Better Sine Wave, which gives you an alternate view of it. So, going back to our 4,500 tick bar chart here, and let’s look at this in terms of the Better Sine Wave indicator. Exactly the same period of time and data.

So, here we go, this is the Hilbert Sine Wave view of the world. And what it says is we’re in a downtrend period here, and we went into a pullback kind of trend where this downtrend actually came to an end. After the end of trend signal, we go through a period of consolidation.

During the period of consolidation here you can see the support, these dynamic support and resistance levels being plotted throughout this entire period here. And then the market breaks out into another trend move when it breaks a resistance or a support level, and pull back to end of trend, this tells us this is a trending period here.

After we get an end of trend signal, we’re going to go through some consolidation. And again, adaptive support and resistance levels being plotted on this data until we break out into another trend here. Pull back to end of trend. The market’s so strong. This was on Friday. The market just keeps on going there. Breaks out into another up trend, so it’s still in a trending phase here.

The Better Sine Wave indicator is showing you periods of consolidation, and periods of trending. And so what you need to do is to figure out what the market is doing and to play it accordingly. If the market is going through a consolidation phase here, having been a strong trend, you need to be playing the support and resistance levels. And then waiting for the next breakout into a trend, which happens to be an up trend here, above this level, and you can ride along the trend.

Now the beauty of using this Better Sine Wave, or this Hilbert Sine Wave approach is that, first of all, there are no inputs to tweak. You just load this onto a chart and it dynamically calculates these support and resistance levels. There are no inputs. Nothing to optimize.

The second thing is, because these levels are dynamically calculated, it’s an improvement on the traditional support and resistance view of the world, where the support and resistance levels were actually fixed values, when people were charting the market. This is calculating these and you can see these move through a fairly wide kind of range, and that the support and resistance levels are not fixed.

So, that’s my pitch for the Better Sine Wave indicator and why you should be ditching moving averages. The moving averages will always be giving you false signals through all these consolidation periods. Great during the trending periods. Lousy during consolidation. Whereas your dynamic Better Sine Wave or Hilbert Sine Wave type view of the world will actually tell you when you’re in one of these congestion zones and when you break out of those congestion zones into trend moves.

Now some of you who are familiar with the older versions of the Better Sine Wave indicator might be thinking: “Hold on, wasn’t there a Jurik Moving Average, a JMA version of the Better Sine Wave? Weren’t you using a moving average then?”

It’s true, yes there was a JMA version, but here’s a little twist and here’s how I was using that particular moving average. I’ve subsequently replaced the JMA with my own version of a fast kind of moving average. But the moving averages were being used to smooth the incoming price data or “pre-process” it in order to eliminate the noise.

You can use that technique to pre-process noisy price data into your other indicators. The difference is that all you’re using is a very short window, a short period for those moving averages. No more than 5 bars and something between 2 and 4 bars is ideal.

In fact, one of the simplest ways to use something like a moving average to pre-process, or smooth, data is to use a 3-bar or a 5-bar median of the price data coming in, in order to get rid of that noise. So, there was a moving average version that I was using, but I was using it in a totally different way. Very short term in order to pre-process data and get out the noise from some of the noisy price data streams that you get.

So, there we go, just a quick video explaining my pitch for why I think you should ditch moving averages. I get lots of charts sent to me by email by traders. If you still continue to use moving averages, I’m not going to hold it against you, but just consider there is an alternate way, and this search for the ultimate moving average I just think – it’s in the wrong direction. We need to be using approaches that are a lot smarter to understand the psychology of the market and try and figure out when we’re trying to break out of support and resistance levels.

Moving Average Parameters

Three Moving Average Parameters

So you want to add a moving average on your charts. What are the parameters you have to set or choose? There are only a few (three):

The prices that will be used for calculating the average: close, average of high and low, average of high, low, and close, etc.

The length of the period of the moving average – how many bars will be used for calculating the moving average, or in other words how many bars back we want to look at every moment.

Type of moving average – the formula used: simple vs. exponential vs. other types.

Let’s now explore each of the parameters.

Parameter 1: Price Used for Moving Average Calculation

Most typically people use every bar’s closing price to calculate moving averages. In many cases this is justified by the special role the closing price has. For example, every day’s closing price of a stock index represents the stock market’s consensus at the end of that trading day, when traders are closing their intraday positions and preparing their portfolios for the night when they will not be looking at the market.

On the other hand, closing prices of bars are much less significant on intraday charts – the information regarding at which price the market was trading exactly at the end of a particular 5 or 10 minute period during the day has little meaning for most market participants. Therefore you can look at alternative methods of calculating moving averages when you are working with intraday data: moving averages can be calculated from the averages of high and low of each bar, or from the so-called typical price (the average of high, low, and close), or from the average of all four prices (open, high, low, and close).

Parameter 2: Moving Average Period Length

The length of the moving average or more precisely the number of bars included in the moving average calculation is probably the most discussed of the three parameters. You can calculate moving average from just a few (e. g. 8) most recent price bars and you will see that it reacts very quickly to every little change in the market’s direction. Alternatively, you can include tens or hundreds of price bars in the calculation (e. g. 200 bars is a popular setup). This way you will filter out all the bar-to-bar noise – the long period moving average will reflect only the meaningful, long-term price trends.

Besides looking at the number of bars . you naturally also have to take into consideration how long each bar is . While 10 bars represent 2 weeks on a daily chart, they are less than one hour on a 5 minute chart.

There is no ideal moving average period length . as different trading styles and strategies require looking at different information. The problem of finding a good moving average period was discussed here: Moving Average Period .

Parameter 3: Moving Average Type

The most common moving average type is simple moving average . As its name suggests, it is also the simplest one to calculate and understand (that’s probably the main reason why it’s the most popular). Simple moving average is (simply) the arithmetic average of the last N bars (N is the moving average period discussed above). You sum up N most recent prices and divide the result by N.

Besides simple moving average, there are other types. There are only little variations in the formulas and sometimes it is difficult to tell which type of moving average it is just by looking at a chart. For example, exponential moving average puts more weight to the most recent prices and therefore it appears to be reacting a bit faster to price changes compared to the simple moving average. Other frequently used moving average types include least-square moving average . adaptive moving average . or weighted moving average . If you are creative and good with numbers, you can even design your own proprietary methods (nevertheless, the usefulness of such effort is questionable, given the little differences and little extra information you get).

Which Moving Average Parameters to Use?

If you have not done much quantitative testing and have no idea which moving average calculation method may be effective for your trading approach, I would suggest you start with the very basic. Take simple moving average calculated from closing prices (this is the setup your charting software most likely has as default) and focus your energy on finding a good moving average period length. Also keep in mind that moving average is just one tool, just one piece of the analysis, and you will probably need to include other things (like the fundamentals, volume, or price action) into your decision making to build a sound trading strategy.

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FX Week USA is returning to New York in July, 2016. This is an essential event for FX traders and other FX industry leaders to discuss the most pressing questions facing the market. FX Week is perfectly positioned to offer the most comprehensive program to educate and create a platform for industry

OpRisk North America is back! Operational Risk & Regulation magazine brings this well established event to operational risk professionals in North America. Attended by leading industry professionals from top tier banks, regulatory organizations, insurance companies and the buy-side.

Date: 14 Mar 2016

New York Marriott Marquis, New York

FX Week Australia is an essential event for FX traders and other FX industry leaders to discuss the most pressing questions facing the market. FX Week is perfectly positioned to offer the most comprehensive program to educate and create a platform for industry networking.

Check the website for details of the 10th annual FX Invest conference for the North America region taking place in Boston, USA. FX Invest North America will bring together leading buy-side practitioners in the fast developing foreign exchange and currency markets. This is a must-attend event

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Structured Products dirige tres programas globales de premios - para las Américas, Asia y Europa - para celebrar la excelencia en los mercados de productos estructurados. The Structured Products awards are the industry's most prestigious honour, designed to recognise the top buyside and sellside firms in the ma

The 2016 Hedge Funds Review 16th Annual European Single Manager Awards recognises the best hedge funds in Europe. The European Single Manager Awards remains the most prestigious event held exclusively for the European hedge fund industry and continues to attract the top names.

The OpRisk Awards recognise the outstanding achievers across the operational risk markets, including banks, insurers, regulators, consultants and vendors. We celebrate the industry's hard work in style and the awards ceremony is a great opportunity to network and find out about the companies perform

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Moving average (MA)

How to set moving average on mt4 chart

Moving average is very important indicators on mt4 chart. Many traders use this MA for technical analysis. In this lesson you will learn how to set moving average indicator on your MetaTrader4 chart.

1. First open your mt4 platform. In the menu bar, click on “ Insert ”. Then click on “ Indicators ”. From right side window, click on “ Trend ”. Then you will see many indicators. Click on “ Moving Average ”.

2. New window will be opened. You will see 3 tab on that window. In Parameters tab, you can set your moving average value on period box. You can change MA method. There are four types of method such as Simple, exponential, smoothed and linear weighted. You can choose as your wish. Simple and exponential MA is very popular. If you select Simple . then your MA will be called SMA. If you set exponential . then MA will be called EMA You can change also apply to such as Close, Open, High, Low and several other options. You can customize MA color from Style .

3. In Level tab, you can set channel with main MA. Click on Add . then double click on Level and put distance value from your MA. This option is not compulsory. You can avoid this parameter or keep the value 00.

4. In visualization tab, you can see the time frame where you can use this moving average. If you select All timeframes . then you will see your MA on all time frames.

5. Thus you can easily set moving average on your chart.

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Time Series - Moving Average - Time series Smoothing.

Unformatted text preview: Time series Smoothing techniques Tim Low April 14, 2015 1/1 Components of a Time Series 2/1 Moving averages The moving average replaces the original time series with another series, each point of which is the center of and the average of N points from the original series. For this reason, this technieque is also known as the centered moving average. The purpose of the moving average is to take away the short term seasonal and irregular variation, leaving behind a combined trend and cyclical movement. We use notation MA(k), to denote a moving average given by a window of k consecutive time periods This technique will be explained through analysis of a time series for a state's electricity purchases. 3/1 Moving averages continued To compute MA(k): The rst moving average of this sequence is obtained by calculating the average of the rst consecutive k values (y1. y2. yk ) The second moving average is obtained by calculating the average of the next batch of consecutive k values excluding the rst value (y2. y3. yk+1 ) The third moving average is obtained by calculating the average of the next batch of consecutive k values excluding the rst and second values (y3. y4. yk+2 ) The process continues until the average of the last batch of k consecutive values is computed. There will be n k + 1 smoothed values 4/1 Moving averages continued Notes: When plotting moving averages on a chart, each of the computed values is plotted against the middle period of the sequence of periods used to compute it. We want to assign each moving average to an instant at which an observation was made. This alignment of time points for the observed and smoothed values is important for plotting the smoothed series Hence when k is even it becomes necessary to average out 2 adjacent MA(k) values (i. e. we centre the moving averages) 5/1 Moving averages continued Subjective choice of k: k should be chosen so as to minimize the uctuations as best as possible. If the data are quarterly, then k = 4 since there are four quarters in a year If the data are daily, then k = 7 since there are seven days in a week The bigger k gets, the smoother the series becomes If k is too large, the smoothed series tends towards a straight line (which defeats the purpose of identifying components of a TS) 6/1 Moving averages example: Electricity purchases - MA(3) Time (t) 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Elec purchase (yt ) 815 826 745 776 838 837 831 858 896 926 946 947 973 977 1008 3-year moving total MA(3) 7/1 Moving averages example: Electricity purchases - MA(3) Time (t) 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Elec purchase (yt ) 815 826 745 776 838 837 831 858 896 926 946 947 973 977 1008 3-year moving total MA(3) 2386 8/1 Moving averages example: Electricity purchases - MA(3) Time (t) 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Elec purchase (yt ) 815 826 745 776 838 837 831 858 896 926 946 947 973 977 1008 3-year moving total MA(3) 2386 2347 9/1 Moving averages example: Electricity purchases - MA(3) Time (t) 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Elec purchase (yt ) 815 826 745 776 838 837 831 858 896 926 946 947 973 977 1008 3-year moving total MA(3) 2386 2347 2359 10 / 1 Moving averages example: Electricity purchases - MA(3) Time (t) 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Elec purchase (yt ) 815 826 745 776 838 837 831 858 896 926 946 947 973 977 1008 3-year moving total MA(3) 2386 2347 2359 2451 2506 2526 2585 2680 2768 2819 2866 2897 2958 795.3 11 / 1 Moving averages example: Electricity purchases - MA(3) Time (t) 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Elec purchase (yt ) 815 826 745 776 838 837 831 858 896 926 946 947 973 977 1008 3-year moving total MA(3) 2386 2347 2359 2451 2506 2526 2585 2680 2768 2819 2866 2897 2958 795.3 782.3 786.3 817.0 835.3 842.0 861.7 893.3 922.7 939.7 955.3 965.7 986.0 12 / 1 Moving averages continued The problem with the moving average technique is that you will also lose k 1 observations if k is odd, and k observations if k is even after the averages have been centred E. g. for MA(3) there is no corresponding moving average value for the rst and last instant and the corresponding observed value. The larger k is, the fewer number of moving averages that can be computed and plotted, thus sometimes making it dicult to obtain an overall impression of the entire series. 13 / 1 Moving averages example: Electricity purchases - MA(4) Time (t) 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Elec purchase (yt ) 815 826 745 776 838 837 831 858 896 926 946 947 973 977 1008 MT(4) MA(4) 14 / 1 Moving averages example: Electricity purchases - MA(4) Time (t) 1995 1996 Elec purchase (yt ) 815 826 1997 1998 1999 2000 2001 2002 MT(4) AMT(4) MA(4) 745 776 838 837 831 858 3162 15 / 1 Moving averages example: Electricity purchases - MA(4) Time (t) 1995 1996 Elec purchase (yt ) 815 826 MT(4) AMT(4) MA(4) 3162 1997 745 3185 1998 1999 2000 2001 2002 776 838 837 831 858 16 / 1 Moving averages example: Electricity purchases - MA(4) Time (t) 1995 1996 Elec purchase (yt ) 815 826 1997 745 1998 776 1999 2000 2001 2002 MT(4) AMT(4) MA(4) 838 837 831 858 3162 3185 3196 17 / 1 Moving averages example: Electricity purchases - MA(4) Time (t) 1995 1996 Elec purchase (yt ) 815 826 1997 745 1998 776 1999 2000 2001 2002 MT(4) AMT(4) MA(4) 838 837 831 858 3162 3173.5 3185 3196 18 / 1 Moving averages example: Electricity purchases - MA(4) Time (t) 1995 1996 Elec purchase (yt ) 815 826 1997 745 1998 776 1999 2000 2001 2002 MT(4) AMT(4) MA(4) 838 837 831 858 3162 3173.5 3185 3190.5 3196 19 / 1 Moving averages example: Electricity purchases - MA(4) Time (t) 1995 1996 Elec purchase (yt ) 815 826 1997 745 1998 776 1999 2000 2001 2002 MT(4) AMT(4) MA(4) 3173.5 793.38 3190.5 797.63 838 837 831 858 3162 3185 3196 20 / 1 Moving averages example: Electricity purchases - MA(4) Time (t) 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Elec purchase (yt ) 815 826 745 776 838 837 831 858 896 926 946 947 973 977 1008 AMT(4) CMA(4) 3173.5 3190.5 3239 3323 3393 3466.5 3568.5 3670.5 3753.5 3817.5 3874 793.38 797.63 809.75 830.75 848.25 866.63 892.13 917.63 938.38 954.38 968.50 21 / 1 Moving averages continued The problem of losing observations in MA smoothing may be addressed by exponential smoothing. 22 / 1 Exponential smoothing Exponential Smoothing derives its name from the fact that it consists of a series of exponentially weighted moving averages Throughout the series, each smoothing calculation is dependent on all previously observed values. St = yt + (1 )St1 for t 1 where: St is the smoothed series is the smoothing constant (0 1) S1 = y1 23 / 1 Exponential smoothing continued The choice of is somewhat subjective, and is made on the basis of how much smoothing is desired. a small value of produces a great deal of smoothing a large value of results in very little smoothing For this course, will always be provided 24 / 1 Exponential smoothing continued Each exponentially smoothed (St ) value is a weighted average of The actual value for that time period The exponentially smoothed value calculated for the previous time period The larger the smoothing constant (), the more importance is given to the acutally value y for the time period 25 / 1 Exponential smoothing example: Electricity purchase Procedure: Select the value of the smoothing constant. For this example let = 0.3 Identify an intitial value for the smoothed curve. It's common practice to start with S1 = y1 The smoothed value for time period 1 (1995) is 815 thousand kilowatt-hours. This initial value will become less important as its eect is "diluted" in subsequent calculations. Calculations on next slide 26 / 1 Exponential smoothing example: Electricity '95 - '98 Time (t) 1995 1996 1997 1998 Elec purchase (yt ) 815 826 745 776 = 0.3 Exponential smoothed purchase 815 818.3 = 0.3(826) + 0.7(815.0) 796.3 = 0.3(745) + 0.7(818.3) 790.2 = 0.3(776) + 0.7(796.3) The tted value for 1998 is: 0.3(actual purchases for 1998) + 0.7(smoothed purchase in 1997) 27 / 1 Exponential smoothing example: Electricity 1995 - 2009 28 / 1 Exponential smoothing example Use = 0.20 to smooth the following series and plot the results on a chart. Original series 10 12 15 18 21 Calculation Exp ( = 0.2) 29 / 1 Exponential smoothing example cont. Use = 0.20 to smooth the following series and plot the results on a chart. Original series 10 12 15 18 21 Calculation 12(0.2) + 10.0(0.8) 15(0.2) + 10.4(0.8) 18(0.2) + 11.32(0.8) 21(0.2) + 12.66(0.8) Exp ( = 0.2) 10.0 10.4 11.32 12.66 14.32 30 / 1 Components of a time series Smoothing techniques eliminate some random variation (and possibly some seasonal variation), and provide a crude picture of the combined T, C and S components that are present in a time series. In order to forecast however, we need more precise estimates of the components. 31 / 1 Components of a time series Note: We will only concern ourselves with estimating the trend and seasonal components in this course, since these two components account for a major proportion of the observed value (yt ) in a time series. For STA2020F, we will not be estimating the cyclical component, and we will avoid examples in which a cyclical component is strong. 32 / 1 33 / 1. View Full Document

Detalles

ALMA moving average

We have done

In attempt to create a new kind of Moving Average with my friend and colleague Dimitrios Kouzis Loukas (because i was a little bit tired of the classical set of MA everybody’s use from the last 10 years), we’ve created this new one (ALMA)..

It removes small price fluctuations and enhances the trend by applying a moving average twice, one from left to right and one from right to left. At the end of this process the phase shift (price lag) commonly associated with moving averages is significantly reduced. Zero-phase digital filtering reduces noise in the signal. Conventional filtering reduces noise in the signal, but add delay.

The ALMA can give some excellent results if you take the time to tweak the parameters (don’t need to explain this part, it will be easy for you to find the right setting in less than hour)..

Arnaud Legoux Moving Average

Since January 2010, the alma moving average has been downloaded more than twenty five thousand times

Because of its kernel that doesnt give too much importance to what happened in the last bar of data, the ALMA moving average filters out very well noise remaining stick to the underlying trend and when it really matters it responds much better than any other know moving averages.

2 a 4 b example 4 moving average process (condition

b Example 4 Moving Average Process (Condition on ) 0 0 = a Consider the simple MA(1) process 1 − − = t t t a a Z θ Por. 1 | | < 1 − + = t t t a Z a L + + + = − − 2 2 1 t t t Z Z Z θθ Let we minimize. ) ( 1 2 * ∑ = = n t t a S ) ( * S to obtain. ) ( ˆ LSE In particular, for given and. 1 Z. 2 K Z n Z. set 1 2 2 1 1 0 0 a Z a Z a a + = = = M 1 − + = n n n a Z a and compute ) ( * S. In general, we can minimize ) ( * S over (-1, 1) by a numerical method such as grid search and Gauss-Newton method. Consider an MA(1) process, 1 − − = t t t a a Z. based on a series of length 4, we observed. 0 1 = Z and. 0 2 = Z 2 3 = Z 1 4 = Z a) Find the least-square estimate of b) Find an estimate of 2 a σ 5

Este es el final de la vista previa. Regístrese para acceder al resto del documento.

Moving Average Analysis

Moving Average Overview

Double Moving Average

This method is based on the calculation of the second moving average. The second moving average is calculated from the average of first moving average, notated by MA (T x T), means MA (T) period from MA (T) period. This method can be used to forecast data with a linear trend component.

The procedure to calculate double moving average is:

Calculate single moving average

Calculate adjustment, which is the difference between single-MA and double-MA , where

Adjust trend from period n to n+m, if you want to forecast m period ahead.

The forecasting value for m period ahead is a n – where it is the adjusted average value for period n – added by the value of multiplication between m and trend component b n .

Moving Average Analysis with Zaitun Time Series

Zaitun Time provides a feature to perform moving average analysis of a time series. Single moving average and double moving average are available. To perform the moving average analysis on a time series variable:

Click Analysis -> Moving Average

Select Variable Dialog appears. Choose a variable you want to analyze with moving average analysis, and then click OK.

The Moving Average form will appear. Choose the moving average method you wish to apply to your variable, and set the moving average order.

To select the analysis result that will be shown on Result View, click the Results button. Check the boxes of any number of Result Views you wish to see. For the Forecasted selection, you have to enter the data step you wish to forecast.

To save residual, predicted or smoothed data from the model as a new variable, click the Storage button. Check the item you wish to save as a new variable, and then type in the new variable name.

After selecting result views and determining whether you want to save the new variable or not, the software will show the Moving Average form again. Click the OK button to finish your analysis and to show the result views.

The result views selected on the previous step will be viewed as several tabs on the Result View panel.

Moving Average Analysis Result

The result views of moving average analysis in Zaitun Time Series are grouped into two categories, they are tables and graphics. The details of them are described here:

Mesas

Model Summary Shows the summary of moving average model.

Moving Average Table Shows actual, MA, predicted and residual values of moving average model.

Forecasted Shows forecasted values from moving average model, as many steps of data you want to forecast.

Graphics

Actual and Predicted Shows a line plot for actual and predicted values of moving average model

Actual and Smoothed Shows a line plot for actual and smoothed values of moving average model.

Actual and Forecasted Shows a line plot for actual and forecasted values of moving average model

Actual vs. Predicted Shows a scatter plot between actual and predicted values

Residual Shows a line plot for residual values of moving average model

Residual vs. Actual Shows a scatter plot between residual and actual values

Residual vs. Predicted Shows a scatter plot between residual and predicted values

The Moving Average block computes the average of a user-determined number of samples of the input signal, which are all evenly-spaced in time. The average is 'moving' in time, because at each sample time the oldest sample is replaced by a new sample, according to the 'last in, first out' principle.

This 'digital moving average filter' is represented by the following equation 1) :

where k is the current sample number (k = 1, 2, 3. ), y is the output signal, u is the input signal, and n s is the total number of samples. The actual time at the k th sample interval equals k * t s . where t s is the sample time.

The user must specify the following block-parameters:

the number of samples n s

the sample time t s

the initial value of the signal.

The initial value of the signal is required in order to prevent transient errors during the first n s samples in a simulation.

1) Notice that in practice, the equation for the moving average filter has been implemented by means of a Discrete State Space block, as follows:

Here, x has been introduced as intermediate 'state variable'. The 'last in, first out' action takes place in the first equation, while the actual averaging is done in the second one. Resolving this equation for a certain sequence of k values will reveil the simple y(k) equation for the moving average filter, which was discussed earlier.

Here is a code that should be helpful for those using technical analysis in trading and want to test strategies in Excel. It computes the simple, linearly weighted and exponential moving average.

Further I will present and explain the steps for creating the form and the VBA code.

Insert a UserForm – Name: MA_Form

Add four Labels from the Toolbox Controls – Captions as per above print screen

Add a ComboBox for the moving average type selection. It was named comboTypeMA

Add two RefEdit controls for the input range and the output range.

Add a TextBox for selecing the moving average period

Add two buttons: Name:buttonSubmit, Caption: Submit and Name:buttonCancel, Caption: Cancel

In order to generate the drop-down list for MA type selection and load the user form, a new module will be inserted with the below code. The ComboBox items with be populated by moving averages types and the user form will be loaded. Option Explicit Sub load_MA_Form() With MA_Form. comboTypeMA. RowSource = "".AddItem "Simple".AddItem "Weighted".AddItem "Exponential" End With MA_Form. Show End Sub

Below is the code attributed to the Submit button.

Private Sub buttonSubmit_Click() Dim inputRange, outputRange As Range The inputRange will contain the price series used for computing the MAs and the outputRange will be populated with the moving averages values.

Dim inputPeriod As Integer The moving average period is declared. Dim inputAddress, outputAddress As String The input and output ranges declared as string. If comboTypeMA. Value <> "Exponential" _ And comboTypeMA. Value <> "Simple" _ And comboTypeMA. Value <> "Weighted" = True Then MsgBox "Please select a moving average type from the list." RefInputRange. SetFocus Exit Sub This part of the procedure enforces the first restrictions regarding the submitted data. If the moving average type is not contained in the drop-down list, the procedure will not proceed to the next step and the user will be prompted to select it again. ElseIf RefInputRange. Value = "" Then MsgBox "Please select the input range." RefInputRange. SetFocus Exit Sub ElseIf RefOutputRange. Value = "" Then MsgBox "Please select the output range." RefOutputRange. SetFocus Exit Sub ElseIf RefInputPeriod. Value = "" Then MsgBox "Please select the moving average period." RefInputPeriod. SetFocus Exit Sub ElseIf Not IsNumeric(RefInputPeriod. Value) Then MsgBox "Moving average period must be a number." RefInputPeriod. SetFocus Exit Sub End If Other restrictions are created. The input range, output range and input period must not be blank. Also, the moving average period must be a number. inputAddress = RefInputRange. Value Set inputRange = Range(inputAddress) outputAddress = RefOutputRange. Value Set outputRange = Range(outputAddress) inputPeriod = RefInputPeriod. Value The arguments for inputRange and outputRange ranges will be inputAddress and outputAddress declared as strings. If inputRange. Columns. Count <> 1 Then MsgBox "Input range can have only one column." RefInputRange. SetFocus Exit Sub The inputRange must contain only one column. ElseIf inputRange. Rows. Count <> outputRange. Rows. Count Then MsgBox "Output range has a different number of rows than the input range." RefInputRange. SetFocus Exit Sub End If The inputRange and outputRange must have an equal number of rows. Dim RowCount As Integer RowCount = inputRange. Rows. Count Dim cRow As Integer ReDim inputarray(1 To RowCount) For cRow = 1 To RowCount inputarray(cRow) = inputRange. Cells(cRow, 1).Value Next cRow inputarray is declared as array and it’s elements correspond to the values from each row of the input range. If inputPeriod > RowCount Then MsgBox "Number of selected observations is " & RowCount & " and the period is " & _ inputPeriod & ". The input range must have a higher or equal amount of elements than the selected period." RefInputRange. SetFocus Exit Sub End If Another restriction is added – The input range must have a higher or equal amount of elements than the period. If inputPeriod <= 0 Then MsgBox "Moving average period must be higher than 0." RefInputPeriod. SetFocus Exit Sub End If The moving average period must be higher than zero. ReDim outputarray(inputPeriod To RowCount) As Variant Also the array dimensions of outputarray are determined. The lower bound of the array is the inputPeriod value and the upper bound is the value of RowCount (the number of elements in the inputRange ).

Below part of the procedure computed the simple moving average, if the selection for comboTypeMA is Simple . 'SMA----------------------------------------- If comboTypeMA. Value = "Simple" Then Dim i, j As Integer Dim temp As Double For i = inputPeriod To RowCount temp = 0 For j = (i - (inputPeriod - 1)) To i temp = temp + inputarray(j) Next j outputarray(i) = temp / inputPeriod outputRange. Cells(i, 1).Value = outputarray(i) Next i outputRange. Cells(0, 1).Value = "SMA(" & inputPeriod & ")" Basically, the procedure computes the moving average of the last x numbers (x equals to the inputPeriod ), starting with the element of the inputarray equal to the inputPeriod . Below is a simplified example, which shows each step of the procedure. In this example, there are four numbers (no_01, no_02, no_03 and no_04) from row 1 to row 4 and the moving average period is 3.

After each new moving average is computed, each cell of the outputRange will take the value from the outputarray . And after all the moving averages are computed, in the cell above outputRange a title will be inserted containing the moving average type and period.

This next part will compute the exponential moving average.

'EMA------------------------------------------ ElseIf comboTypeMA. Value = "Exponential" Then Dim alpha As Double alpha = 2 / (inputPeriod + 1) For j = 1 To inputPeriod temp = temp + inputarray(j) Next j outputarray(inputPeriod) = temp / inputPeriod First the value of alpha is determined. Because in the computation, the value of the EMA is based on the previous EMA, the first one will be the simple moving average. For i = inputPeriod + 1 To RowCount outputarray(i) = outputarray(i - 1) + alpha * (inputarray(i) - outputarray(i - 1)) Next i Starting with the second moving average, they will be computed based on the above formula: the previous EMA plus alpha multiplied by the difference between the current number from the inputarray and the previous EMA value. For i = inputPeriod To RowCount outputRange. Cells(i, 1).Value = outputarray(i) Next i outputRange. Cells(0, 1).Value = "EMA(" & inputPeriod & ")" Just like the code for SMA, the outputarray will be populated and the cell above outputarray will represent the type and period of the moving average.

Below is the code for computing the weighted moving average.

'WMA------------------------------------------ ElseIf comboTypeMA. Value = "Weighted" Then Dim temp2 As Integer For i = inputPeriod To RowCount temp = 0 temp2 = 0 For j = (i - (inputPeriod - 1)) To i temp = temp + inputarray(j) * (j - i + inputPeriod) temp2 = temp2 + (j - i + inputPeriod) Next j outputarray(i) = temp / temp2 outputRange. Cells(i, 1).Value = outputarray(i) Next i outputRange. Cells(0, 1).Value = "WMA(" & inputPeriod & ")" End If

The below table contains the steps for computing each variable used for the WMA computation. Just like in the previous example, in this one there are for numbers in the inputRange . and the input period is 3.

Below is the final code of the procedure, which unloads the user form. Unload MA_Form End Sub

The below procedure is for the Cancel button. It will be added in the same module. Private Sub buttonCancel_Click() Unload MA_Form End Sub

Moving Average - Price Graph

The number of moving averages, as well as the length of time to average over, are adjustable with the Moving Average for Graphs Dialog .

The graph will be labeled with MA-NAV to stand for Moving Average - Net Asset Value. The ending moving averages are displayed on the legend and will be labeled with the length in weeks of the moving average. The change in these values from the previous day is also displayed in parenthesis. The legend for each line is shown in the same color as the associated moving average line. The colors of each moving average can be adjusted with the Graph Colors Dialog and the "Overlaid/MA" line selections.

If the yields are turned on ( View / Yields ) they will be displayed above the graphs. See Yield Calculations for information on the reported yields.

Ver también

Advanced trading software: technical analysis and neural networks

Ingenious Moving Average: Optimizing Technical Analysis

Being a trader, you are probably familiar with the constant attempts to create the ideal Moving Average (MA), capable of sufficiently reducing excessive noise, have resulted in: the noise is still there.

Sin embargo, no todas las noticias son malas. Inspirado por la incansable investigación, conducida por Kalman, Kaufman, Jurik y otros talentosos analistas de mercado, comerciantes y científicos, el equipo de investigación de Tradecision se negó a ser desalentado por la situación. Esta perseverancia no fue en vano. No es que hayamos creado algo perfecto. We have just managed to develop a noise-elimination filter that gives the trader a much better insight into the market situation, better than any other MA’s we know – Ingenious Moving Average . Let us spare you the marketing mumbo-jumbo and get down to the facts by looking at several examples of Ingenious MA’s performance.

The analysis will consider the filter’s performance using the 3 main measurements of any MA’s performance: accuracy, timeliness, and smoothness.

Accuracy Since accuracy is responsible for how close to the original data a graph line produced by a moving average is, it is opposed to another of the 3 parameters – smoothness. Cuanto más suave sea el MA, más flojamente refleja la serie de tiempo original. Por lo tanto, una MA precisa debe asegurar la correlación más óptima de los dos parámetros. En este sentido, Ingenious MA eclipsa cualquier otro MA en existencia.

Oportunidad Otro aspecto crucial sobre el cual se evalúa cualquier MA es la cantidad de retraso que tiene. El uso de una MA significativamente rezagada detrás de la serie de tiempo original puede resultar muy fácilmente en tomar decisiones tardías y perder así sus operaciones. Dado que una MA totalmente libre de retrasos no puede existir incluso teóricamente, Ingenious MA puede considerarse el MA con el cual la cantidad de lag se reduce óptimamente.

Suavidad Sin lugar a dudas, la suavidad se considera el factor de rendimiento más importante, simplemente porque cualquier tipo de filtro destinado a eliminar el ruido también debe hacer que su gráfico óptimamente suave. Como ya hemos mencionado anteriormente, la suavidad es contrarrestada por la precisión, y asegurar un nivel óptimo de suavidad sin sacrificar la precisión de una MA es el obstáculo clave. Hemos cumplido con ese desafío crucial encendido encendido con mucho éxito.

Download the Ingenious Moving Average article (a PDF file; 140 KB).

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What is the DIG MA Types Indicator?

Our programmers have brought together the 8 best Moving Averages and bundled them together into one amazing indicator, making them easy to use and absolutely stunning on the charts. Furthermore we have coded in a unique channel feature that can be turned on and off.

Which Moving Averages do DIG MA Types support?

EMA – Exponential Moving Average – Low lag.

SMA – Simple Moving Average – Standard simple moving average.

WMA – Weighted Moving Average – Provides greater value to new prices.

HMA – DIG Hull Moving Average – Supper Low Lag, quick response and very smooth.

TMA – Triple Moving Average – Quick Response, supper smooth.

SMA3 – Triple Simple Moving Average – Almost none overshot, great for trends.

KF – Kalman Filter Moving Average – High reliability.

Gauss – Gauss Moving Average – Long time frame support.

How to choose the right MA for you?

Most traders like to stick to the standard MA types – Simple and Exponential, these 2 are incredible, but if you are only familiar with them you might be missing out. If you plan to use the MA as a trigger then it is more important to have it respond quickly and be smooth, in such as case choose low lag MAs, but if you plan to use the MA as a setup then it is more important to have it keep trend, not overshoot.

Examples: HMA – DIG Hull Moving Average – Supper Low Lag, quick response and very smooth. S&P500 Futures 15 Min Chart: Notice how the MA in this case our DIG Hull Moving Average is color coded according to its direction making it much to read at one glance. Also notice now quickly it reacts to change yet how stable the change in directionality is – great for signals.

MLNX Daily Chart: In this case we have long length MA for overall trend understanding, we use the Gauss MA, notice how stable it is providing a great overall trend.

EURUSD Forex 15 Min Chart: In this case we have an Exponential moving average with the Channel feature enabled, in this case set to pips ( can also be set to percent ).

8 Different MA Types in one amazing indicator.

New Feature – Color Coded according to trend.

Easy to use and support any chart and any timeframe.

New Feature – On/Off channel plotting.

Download DIG MA Types For Free!

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The formula for calculating a moving average is as

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Unformatted text preview: The formula for calculating a moving average is as follows: MA n = D t t = 1 n n (1) where n = number of periods in moving average and D t = data in period t. 2.1.1 Moving Average Example Using Excel Functions For example, a restaurant that features smoked ribs wants to forecast sales for the next year. In this example the restaurant manager has actual sales data for each of the last twenty-two years. Using this scenario the manager employs a three and five-year moving average to forecast the next year's sales figure. The mathematical equation for the three-year moving average is expressed as: MA(3) = M t + 1 = D t + D t 1 + D t 2 ( ) 3 2 Spreadsheets in Education (eJSiE), Vol. 2, Iss. 2 [2007], Art. 5 http://epublications. bond. edu. au/ejsie/vol2/iss2/5 FORECASTING WITH EXCEL: SUGGESTIONS FOR MANAGERS 214 whereas the five-year moving average is MA(5) = M t + 1 = D t + D t 1 + D t 2 + D t 3 + D t 4 ( ) 5 where MA(3) is the moving average using 3 periods of data, MA(5) is the moving aver-age using 5 periods of data and D is demand and t is time. Table 1: Sales Data Set for Rib Sales Year Sales ($000) Year Sales ($000) 1980 52.04 1991 83.18 1981 59.42 1992 87.05 1982 55.66 1993 84.79 1983 53.86 1994 73.49 1984 64.59 1995 76.23 1985 75.28 1996 96.54 1986 61.89 1997 95.08 1987 73.74 1998 87.05 1988 81.19 1999 96.02 1989 97.52 2000 98.90 1990 86.50 2001 83.23 The MA(3) and MA(5) forecasts are created manually via the following formulae in Excel (see Figure 1). Figure 1: Moving Average Formulae in Excel 3 Nadler and Kros: Forecasting with Excel: Suggestions for Managers Produced by The Berkeley Electronic Press, 2007 S. NADLER AND J. F. KROS 215 The actual forecasts can be found in Figure 2 and Figure 3. Based on this analysis the manager would forecast $92,720 in sales using the three-year moving average and $92,060 in sales using the five-year moving average. 50 55 60 65 70 75 80 85 90 95 100 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 Year Sales ($000) 3-Year MA 5-Year MA Figure 2: Graph of Actual Sales, MA(3) Sales Forecast. and MA(5) Sales Forecast 2.1.2 Moving Average Example Using Excel's Data Analysis Add-In To illustrate the concept of forecasting using moving averages, let's analyze the data set listed in Table 1. We will demonstrate a three-year and five-year moving using Ex-cel's Moving Average tool. The following steps should be completed to create a moving average in Excel: 1. Be sure to have Excel's Data Analysis package loaded (see Microsoft Help menu) 2. Choose the Tools menu in Excel and then the Data Analysis option (see Figure 4), a new menu resembling Figure 5 will appear on screen. 4 Spreadsheets in Education (eJSiE), Vol. 2, Iss. 2 [2007], Art. 5 http://epublications. bond. edu. au/ejsie/vol2/iss2/5 FORECASTING WITH EXCEL: SUGGESTIONS FOR MANAGERS 216 Figure 3: MA(3) and MA(5) Sales Forecasts Figure 4: Tools Menu in Excel 3. From the dialog box displayed in Figure 5, choose Moving Average and click. Ver documento completo

Detalles

Making Sense of Moving Averages

BALTIMORE (Stockpickr) - En el mundo del análisis técnico, el promedio móvil, o MA, bien puede ser el indicador más popular por ahí. Pero con demasiada frecuencia, los técnicos nacientes del mercado sólo tienen una comprensión pasajera del mensaje que las líneas añadidas en sus cartas técnicas les están diciendo.

Hoy, vamos a echar un vistazo a cómo funcionan las medias móviles - y cómo pueden señalar las operaciones en el mundo real.

Los promedios móviles apenas quedan relegados al mundo del comercio. In fact, it's a common statistical tool that's used to interpret large time series datasets by making piecemeal data points relatable to the whole; Matemáticamente, los promedios móviles son operaciones de suavizado que igualan los valores atípicos estadísticos y dan una imagen más clara sobre el conjunto de datos que se está examinando.

What that essentially means is that moving averages can take a potentially volatile item like a stock price, and give investors a graph that's much more indicative of the stock's overall movement. MA corte a través del ruido del mercado.

To put it simply, the moving average is just a rolling average - that is, it's the average price of a stock over a given number of days. Every day, the most recent day's data gets added to the moving average and the last day's data falls off.

Moving Average Weighting Woes

Pero los técnicos pronto descubrieron una falla importante en este simple promedio móvil (SMA): ponderación. Después de todo, los datos de precios de hace casi un año (en el caso de la siempre popular media móvil de 200 días) no eran tan relevantes para el mercado de hoy como el precio de ayer; Pero ambos tuvieron un impacto igual en el valor de la media móvil.

Para remediar eso, la media móvil exponencial, o EMA, se convirtió en una alternativa popular. Unlike the simple moving average, where each day's prices held the same impact, the EMA is calculated such that each day's significance decreases exponentially. Mientras que otros esquemas de ponderación existen, la SMA y EMA son de lejos el más popular en uso por los analistas técnicos de hoy.

El período de tiempo de la media móvil es también un elemento crucial. The most popular alternatives include the 9-day, 50-day, and 200-day moving averages (simple or exponential, depending on the application as well as the trader's preference). Pero mientras que las medias móviles diarias, que representan el precio de una acción sobre los X días que se arrastran, son comunes, es esencial recordar que las medias móviles se pueden utilizar para cualquier período de tiempo.

Probably the most frequently used indicator in technical analysis is the moving average. The concept of a moving average is that it shows the average value of a pair’s price over a set period. In other words, it measures what the average price of the pair is over a certain amount of candles. You may have a 20-day moving average placed on your chart, which will show itself in the form of a line. This line plots the average price of the pair over the last 20 candles, in this example – 20 days. Moving averages are often used to spot momentum and define possible support and resistance areas in a currency pair.

Moving averages are used to define the direction of a currency pair (its trend) and to help smooth out price fluctuations, sometimes called "noise" that can make determining the trend difficult in certain circumstances. As a general rule, bullish or upward momentum is confirmed when a shorter-term moving average (as an example, 10-day moving average) crosses above a longer-term average (perhaps a 25-day moving average). Downward momentum is confirmed when the shorter-term moving average crosses below the longer-term one.

While there are different types of moving averages, they are all used in the same general ways. The two most common types of moving averages that you will come across trading Forex are the simple moving average and exponential moving averages. The simple moving average is calculated using the simple formula of adding all of the values together, and dividing it by the period you are using. In other words, you simply add up all of the closing prices over the last (x) candles, and dividing it by that number. The exponential moving average is calculated in a complex manner that gives greater weight in the calculations to the most recent candles. Because of this, the exponential moving average is considered to be more predictive in a shorter-term chart, while the simple moving average will be slower to change, making it a better “smoothing mechanism”.

High Risk Investment Warning: Trading FOREX on margin carries a high level of risk, and may not be suitable for all investors because the high degree of leverage can work against you as well as for you. Before deciding to trade FOREX you should carefully consider your investment objectives, level of experience, and risk appetite. The possibility exists that you could sustain a loss of some or all your initial investment and therefore you should not invest money that you cannot afford to lose. You should be aware of the risks associated with FOREX trading, and seek advice from an independent financial advisor if you have any doubts. Please read the full disclosure below:

Moving Average (MA)

The MA indicator ( Moving Average indicator ) is one of the oldest technical modern indicators and the most often used indicator in technical analysis.

A moving average is an average of a shifting body of data, as seen from its name. For example, a 10-day moving average is got by adding closing prices for the last 10 periods being measured and dividing by 10. The term "moving" is used as only the last 10 days are used in the measurement. That's why the data body is averaged shifted forward with every next trading day.

The moving average line will be placed directly in the price shifting chart. The moving average is measured with a definite predefined period. La sensibilidad del promedio móvil es más débil si el período es más largo. La probabilidad de señales falsas es mayor si el período es más corto.

On the whole, the moving average is a smoothing tool. Los precios bajos y altos se oscurecen y la tendencia básica del mercado se ve más precisamente haciendo un promedio de la información de precios. But by its very nature the moving average line is behind the market action. Una media móvil más corta (3-5 días) abrazaría la acción del precio más de cerca que una media móvil de 40 días. Shorter term moving averages are more influenced by everyday shifts.

Moving Average demonstrates the average value of a security's price in a time frame. The average price shifts up or down when the security's price shifts.

There are 5 popular types of moving averages: simple (or arithmetic), variable exponential, weighted and triangular. You can measure moving averages on any data series comprising a security's open, volume, high, low, close or any other indicator. The basic distinction between MA variants is the weight which refers to the latest data.

Los promedios móviles simples proporcionan el mismo peso a todos los precios. Triangular averages provide more weight to prices in the middle of the time period. Los promedios exponenciales y ponderados proporcionan más peso a los precios recientes.

To interpret a moving average usually you should just compare the links between a moving average of the security's price with the security's price itself. If the security's price rises above its moving average a purchase signal is generated. If the security's price shifts below its moving average a sell signal is generated.

In other words, the interpretation of an indicator's moving average is the same as the interpretation of a security's moving average. Una vez que el indicador se mueve por debajo de su media móvil, significa un movimiento hacia abajo de larga duración por el indicador, y si el indicador se mueve por encima de su promedio móvil, significa un movimiento hacia arriba de larga duración por el indicador.

The MACD, Price ROC, Momentum, and Stochastics are among the indicators which are best-suited for usage with moving average penetration systems. Some indicators, such as short-term Stochastics, change so erratically that it is difficult to see their real trend. If you want to see the basic trend of the indicator more than its everyday changes you can erase the indicator and then placing a moving average of the indicator.

Mediante la colocación de una media móvil a corto plazo (2-10 días) de los indicadores de oscilación como Stochatics, el ROC de 12 días o el RSI whipsaws se puede reducir, a expensas de las señales un poco más tarde. For instance, it's possible to sell only when a 5-period moving average of the Stochastic Oscillator moves below 80 rather than selling when the Stochastic Oscillator falls below 80.

Jan 8, 2009: 10:02 AM CST

A few readers have asked about the difference between Simple and Exponential Moving Averages and I wanted to address that in an educational post.

In my charting, I utilize the 20 and 50 period Exponential Moving Average (EMA) and also the 200 period Simple Moving Average (SMA). I do this because I want the shorter averages to track the prices closer – and I’m interested in the spread along with the ‘orientation’ of the 20 and 50 EMAs, but I also want to see an average price over the last 200 trading days that is unweighted, thus I use the SMA for longer-term purposes. Also, many funds follow the 200 day or week SMA and that might be all the technical analysis they use, so it tends to cause ‘reactions’ and is an important level to watch.

I like to use the 20 and 50 EMAs to help determine structure (uptrend/downtrend) and also to develop low-risk, high probability trade set-ups (entries) in a trending environment (buying pullbacks to the 20 or 50 EMA in a rising trend, for example).

So what is the difference between Simple and Exponential Averages?

Rather than recreate the wheel for you, I want to direct you to the most comprehensive free resource on moving averages I’ve seen on the web, which is StockCharts. com’s article on Moving Averages. Here are a few key points pulled from that article:

“A simple moving average is formed by computing the average (mean) price of a security over a specified number of periods.

Exponential Moving Averages reduce the lag by applying more weight to recent prices relative to older prices. In order to reduce the lag in simple moving averages, technicians often use EMAs.

The initial thought for some is that greater sensitivity and quicker signals are bound to be beneficial. This is not always true and brings up a great dilemma for the technical analyst: the trade off between sensitivity and reliability.

All moving averages are lagging indicators and will always be “behind” the price. Cuando los precios son tendencia, las medias móviles funcionan bien. However, when prices are not trending, moving averages can give misleading signals.”

In sum: “The exponential moving average is consistently closer to the actual price.”

Good question! I wanted to quote from the StreetAuthority. com’s MA Article for a succinct answer:

“What is the purpose of the exponential moving average? Moving averages are lagging indicators, and therefore, by definition, will give late signals. By weighting recent price data more heavily . exponential moving averages attempt to speed up the signal given . The disadvantage of doing this, of course, is that this more-rapid signal can sometimes be premature and therefore give the swing trader a false indication to trade.”

Ultimately, it comes down to your experience and even the character of a given security – some tend to ‘work’ better with SMAs while others do so with EMAs – it takes practice and experience to find the balance that works for you. There are no quick answers unfortunately.

Through my experience and trading style, I’ve compromised and settled on the 20 and 50 EMAs along with the 200 SMAs, though I know many traders who do quite well with many other combinations.

Browse these two articles for full details and feel free to share your experiences in the comment section so we can learn from each other.

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Weighted Moving Average

In Example 1 of Simple Moving Average Forecast. the weights given to the previous three values were all equal. We now consider the case where these weights can be different. This type of forecasting is called weighted moving average . Here we assign m weights w 1 . …, w m . where w 1 + …. + w m = 1, and define the forecasted values as follows

Ejemplo 1 . Redo Example 1 of Simple Moving Average Forecast where we assume that more recent observations are weighted more than older observations, using the weights w 1 = .6, w 2 = .3 and w 3 = .1 (as shown in range G4:G6 of Figure 1).

Figure 1 – Weighted Moving Averages

The formulas in Figure 1 are the same as those in Figure 1 of Simple Moving Average Forecast. except for the forecasted y values in column C. E. g. the formula in cell C7 is now =SUMPRODUCT(B4:B6,G$4:G$6).

The forecast for the next value in the time series is now 81.3 (cell C19), by using the formula =SUMPRODUCT(B16:B18,G$4:G$6).

Real Statistics Data Analysis Tool . Excel doesn’t provide a weighted moving averages data analysis tool. Instead, you can use the Real Statistics Weighted Moving Averages data analysis tool.

To use this tool for Example 1, press Ctr-m . choose the Time Series option from the main menu and then the Basic forecasting methods option from the dialog box that appears. Fill in the dialog box that appears as shown in Figure 5 of Simple Moving Average Forecast. but this time choose the Weighted Moving Averages option and fill in the Weights Range with G4:G6 (note that no column heading is included for the weights range). None of Parameter values are used (essentially # of Lags will be the number of rows in the weights range and # of Seasons and # of Forecasts will default to 1).

The output will look just like the output in Figure 2 of Simple Moving Average Forecast. except that the weights will be used in calculating the forecast values.

Example 2 . Use Solver to calculate the weights which produce the lowest mean squared error MSE.

Using the formulas in Figure 1, select Data > Analysis|Solver and fill in the dialog box as shown in Figure 2.

Figure 2 – Solver dialog box

Note that we need to constrain the sum of the weights to be 1, which we do by clicking on the Add button. This brings up the Add Constraint dialog box, which we fill in as shown in Figure 3 and then click on the OK button.

Figure 3 – Add Constraint dialog box

We next click on the Solve button (on Figure 2), which modifies the data in Figure 1 as shown in Figure 4.

Figure 4 – Solver Optimization

As can be seen from Figure 4, Solver changes the weights to 0. 223757 and .776243 in order to minimize the value of MSE. As you can see, the minimized value of 184.688 (cell E21 of Figure 4) is at least less than the MSE value of 191.366 in cell E21 of Figure 2). To lock in these weights you need to click on the OK button of the Solver Results dialog box shown in Figure 4.

Hope this is the right forum guys, if not apologies. I'm watching the FTSE with 5 min candles and simple Moving Averages (4, 9 and 19 - Am trying out a technique I've read) and std MACD and histogram settings of 26, 12 and 9.

With it, every time the SP rises, the MACD crosses down below the signal line (when I expect it to cross up over it, not everytime i know, but the majority), it just seems to go the complete opposite direction. Am I doing something wrong please?

I've done 2 x screenshots and saved to a word doc, hopefully its uploaded

Dont all shoot me down, I'm still fairly new to this :)

Admin Guide 79 comments

One of the most widely watched and popular Forex indicator is the 200-day simple moving average SMA. Traders often look to this line to determine When using spot rate and moving average cross over trading signals, it is important to keep two points in mind. Depending on market volatility, cross overs can be. What Is A Moving Average The Moving Average, MA for short, is probably the most popular trend following indicator used by Forex traders, here's what.

Popular moving averages forex

Forex broker choice;. Home Technical analysis Technical indicators Moving Average MA. There are 5 popular types of moving averages simple. A menudo en Forex, los comerciantes se fijan en los promedios móviles intradía. For example, if you're looking at a 10 minute chart and wanted a five-period moving average you could. Moving averages MA's are one of the most popular technical analysis tools used when trading forex. Moving averages lag price, in other words, if price starts to.

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It’s hard to beat Moving Averages for their simplicity in keeping your focus on the trend and taking you out of the trend when you Popular Videos - Moving average & Trading strategy by #MovingAverage; 53 videos; 1,731 views; Last updated on Dec 9, 2015;. Moving Average Forex Trading Strategy

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The two most popular types of moving averages are the Simple Moving. A simple moving average is formed by computing the average price of a security over a specific. Popular moving averages used in forex trading are 5-day a week of price. The next most popular moving average used in the currency trading is called exponential.

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Thursday, December 22, 2016

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