MovingAverages {TTR} | R Documentation |
Calculate various moving averages (MA) of a series.
SMA(x, n=10) EMA(x, n=10, wilder=FALSE, ratio=NULL) WMA(x, n=10, wts=1:n) DEMA(x, n=10) EVWMA(price, volume, n=10) ZLEMA(x, n=10, ratio=NULL)
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. |
ratio |
A smoothing/decay ratio to use (overrides wilder in EMA) |
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 = 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 (default) to minimize
the cumulative effect.
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. |
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.
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
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.
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 ## (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 )