MovingAverages {TTR} R Documentation

## Moving Averages

### Description

Calculate various moving averages (MA) of a series.

### Usage

```  SMA(x, n=10)
EMA(x, n=10, wilder=FALSE)
WMA(x, n=10, wts=1:n)
DEMA(x, n=10)
EVWMA(price, volume, n=10)
ZLEMA(x, n=10)
```

### Arguments

 `x` Vector to be averaged. `price` Vector of prices to be averaged. `volume` Volume series corresponding to price series, or a constant. See Notes. `n` Number of periods to average over. `wts` Vector of weights. Length of `wts` vector must equal the length of `x`, or `n` (the default). `wilder` logical; if `TRUE`, a Welles Wilder type EMA will be calculated; see notes.

### Details

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 the values of `wts` as weights.

DEMA is calculated as: `DEMA = 2 * EMA(x,n) - EMA(EMA(x,n),n)`.

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 to minimize the cumulative effect.

### Value

 `SMA` Simple moving average. `EMA` Exponential moving average. `WMA` Weighted moving average. `DEMA` Double-exponential moving average. `EVWMA` Elastic, volume-weighted moving average. `ZLEMA` Zero lag exponential moving average.

### Warning

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.

### Note

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.

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.

Josh Ulrich

### References

The following site(s) were used to code/document this indicator:
http://www.fmlabs.com/reference/ExpMA.htm
http://www.fmlabs.com/reference/WeightedMA.htm
http://www.fmlabs.com/reference/DEMA.htm
http://linnsoft.com/tour/techind/evwma.htm
http://www.fmlabs.com/reference/ZeroLagExpMA.htm

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

### Examples

```  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"], 20)
zlema.20 <- ZLEMA(ttrc[,"Close"], 20)

## Example of short-term instability of EMA
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 )
```

[Package TTR version 0.13 Index]