Dataplot Vol 2 Vol 1

# EXPONENTIAL SMOOTHING

Name:
EXPONENTIAL SMOOTHING (LET)
Type:
Let Subcommand
Purpose:
Apply exponential smoothing to a time series.
Description:
Exponential smoothing is defined as:

Y2(1) = Y(1)
Y2(I) = ALPHA*Y(I) + (1-ALPHA)*Y2(I-1), I > 1

where Y is the original series and Y2 is the smoothed series.

That is, the current smoothed value is a weighted average of the current point and the previous smoothed point. ALPHA is the smoothing parameter that defines the weighting and should be greater than 0 and less than 1. ALPHA equal 0 sets the current smoothed point to the previous smoothed value and ALPHA equal 1 sets the current smoothed point to the current point (i.e., the smoothed series is the original series). The closer ALPHA is to 1, the less the prior data points enter into the smooth. In practice, ALPHA is usually set to a value between 0.1 and 0.3.

Syntax:
LET <y2> = EXPONENTIAL SMOOTHING <y1>
<SUBSET/EXCEPT/FOR qualification>
where <y1> is a response variable;
<alpha> is a number or parameter that specifies the value of the smoothing parameter ALPHA;
<y2> is a variable where the computed exponential smoothing is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET Y2 = EXPONENTIAL SMOOTHING Y1 0.3
LET Y2 = EXPONENTIAL SMOOTHING Y1 0.8
Note:
If the value of ALPHA is omitted, Dataplot will attempt to find an optimal value (up to 3 decimal places). Note that a brute force method is employed, so this is not a mathematically optimized value. However, the computed value should be adequate for most applications.

In most cases, exponential smoothing is not sensitive to minor departures from the optimal value of ALPHA. That is, determining ALPHA to the first or second decimal place is usually sufficient.

Note:
Exponential smoothing should not be applied to series that contain significant trend or seasonal components.

Holt-Winters smoothing is an extension of exponential smoothing that has trend and seasonal components. Dataplot does not support Holt-Winters smoothing at this time. Dataplot does support seasonal lowess, which is a locally weighted least squares approach to performing a trend, seasonal, residual decomposition of a time series (which is what the Holt-Winters method does).

Note:
Exponential smoothing is an optimal model if the underlying series is a first order moving average model with first differencing applied (i.e., an ARIMA(0,1,1) model). Enter HELP ARMA for details on how Dataplot fits ARIMA models.
Default:
None
Synonyms:
None
Related Commands:
 SMOOTH = Perform least squares smoothing. ARMA = Fit an autoregressive-moving average model. LOWESS = Perform locally weighted least squares smoothing. SEASONAL LOESS = Compute a locally weighted least squares based trend-seasonal-residual decomposition. SPECTRAL PLOT = Generate a spectral plot. AUTOCORRELATION PLOT = Generate a spectral plot.
Applications:
Time Series
Implementation Date:
2000/8
Program:
SKIP 25