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.
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.
LET Y2 = EXPONENTIAL SMOOTHING Y1 0.8
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.
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).
READ LEW.DAT Y
LET Y2 = EXPONENTIAL SMOOTHING Y1 0.3
Date created: 6/5/2001