Moving Averages

Calculate various moving averages (MA) of a series.

SMA(x, n = 10, ...)

EMA(x, n = 10, wilder = FALSE, ratio = NULL, ...)

DEMA(x, n = 10, v = 1, wilder = FALSE, ratio = NULL)

WMA(x, n = 10, wts = 1:n, ...)

EVWMA(price, volume, n = 10, ...)

ZLEMA(x, n = 10, ratio = NULL, ...)

VWAP(price, volume, n = 10, ...)

VMA(x, w, ratio = 1, ...)

HMA(x, n = 20, ...)

ALMA(x, n = 9, offset = 0.85, sigma = 6, ...)


Price, volume, etc. series that is coercible to xts or matrix.


Number of periods to average over.


logical; if TRUE, a Welles Wilder type EMA will be calculated; see notes.


A smoothing/decay ratio. ratio overrides wilder in EMA, and provides additional smoothing in VMA.


The 'volume factor' (a number in [0,1]). See Notes.


Vector of weights. Length of wts vector must equal the length of x, or n (the default).


Price series that is coercible to xts or matrix.


Volume series that is coercible to xts or matrix, that corresponds to price series, or a constant. See Notes.


Vector of weights (in [0,1]) the same length as x.


Percentile at which the center of the distribution should occur.


Standard deviation of the distribution.

any other passthrough parameters


SMA calculates the arithmetic mean of the series over the past n observations.

EMA calculates an exponentially-weighted mean, giving more weight to recent observations. See Warning section below.

WMA is similar to an EMA, but with linear weighting if the length of wts is equal to n. If the length of wts is equal to the length of x, the WMA will use the values of wts as weights.

DEMA is calculated as: DEMA = (1 + v) * EMA(x,n) - EMA(EMA(x,n),n) * v (with the corresponding wilder and ratio arguments).

EVWMA uses volume to define the period of the MA.

ZLEMA is similar to an EMA, as it gives more weight to recent observations, but attempts to remove lag by subtracting data prior to (n-1)/2 periods (default) to minimize the cumulative effect.

VWMA and VWAP calculate the volume-weighted moving average price.

VMA calculate a variable-length moving average based on the absolute value of w. Higher (lower) values of w will cause VMA to react faster (slower).

HMA a WMA of the difference of two other WMAs, making it very reponsive.

ALMA inspired by Gaussian filters. Tends to put less weight on most recent observations, reducing tendency to overshoot.


A object of the same class as x or price or a vector (if try.xts fails) containing the columns:


Simple moving average.


Exponential moving average.


Weighted moving average.


Double-exponential moving average.


Elastic, volume-weighted moving average.


Zero lag exponential moving average.


Volume-weighed moving average (same as VWAP).


Volume-weighed average price (same as VWMA).


Variable-length moving average.


Hull moving average.


Arnaud Legoux moving average.


For EMA, wilder=FALSE (the default) uses an exponential smoothing ratio of 2/(n+1), while wilder=TRUE uses Welles Wilder's exponential smoothing ratio of 1/n.

Since WMA can accept a weight vector of length equal to the length of x or of length n, it can be used as a regular weighted moving average (in the case wts=1:n) or as a moving average weighted by volume, another indicator, etc.

Since DEMA allows adjusting v, it is technically Tim Tillson's generalized DEMA (GD). When v=1 (the default), the result is the standard DEMA. When v=0, the result is a regular EMA. All other values of v return the GD result. This function can be used to calculate Tillson's T3 indicator (see example below). Thanks to John Gavin for suggesting the generalization.

For EVWMA, if volume is a series, n should be chosen so the sum of the volume for n periods approximates the total number of outstanding shares for the security being averaged. If volume is a constant, it should represent the total number of outstanding shares for the security being averaged.


Some indicators (e.g. EMA, DEMA, EVWMA, etc.) are calculated using the indicators' own previous values, and are therefore unstable in the short-term. As the indicator receives more data, its output becomes more stable. See example below.


The following site(s) were used to code/document this indicator:

See Also

See wilderSum, which is used in calculating a Welles Wilder type MA.

  • ALMA
  • DEMA
  • EMA
  • GD
  • HMA
  • MA
  • MovingAverages
  • SMA
  • T3
  • VMA
  • VWAP
  • VWMA
  • WMA
library(TTR) # NOT RUN { data(ttrc) ema.20 <- EMA(ttrc[,"Close"], 20) sma.20 <- SMA(ttrc[,"Close"], 20) dema.20 <- DEMA(ttrc[,"Close"], 20) evwma.20 <- EVWMA(ttrc[,"Close"], ttrc[,"Volume"], 20) zlema.20 <- ZLEMA(ttrc[,"Close"], 20) alma <- ALMA(ttrc[,"Close"]) hma <- HMA(ttrc[,"Close"]) ## Example of Tim Tillson's T3 indicator T3 <- function(x, n=10, v=1) DEMA(DEMA(DEMA(x,n,v),n,v),n,v) t3 <- T3(ttrc[,"Close"]) ## Example of short-term instability of EMA ## (and other indicators mentioned above) x <- rnorm(100) tail( EMA(x[90:100],10), 1 ) tail( EMA(x[70:100],10), 1 ) tail( EMA(x[50:100],10), 1 ) tail( EMA(x[30:100],10), 1 ) tail( EMA(x[10:100],10), 1 ) tail( EMA(x[ 1:100],10), 1 ) # }
Documentation reproduced from package TTR, version 0.23-1, License: GPL-2

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