Exponential smoothing is a family of methods for forecasting a time series in which past observations receive geometrically decreasing weights. In
simple exponential smoothing, the smoothed level 
is the current estimate of
the locally varying baseline of the time series. It
is updated by the recurrence equation
 |
where 
.
Thus 
is a weighted average of the newest observation
and the preceding smoothed level 
; larger 
makes it respond more quickly to new data. The one-step-ahead
forecast is 
.
Expanding the recurrence equation shows that
receives weight 
,
in addition to a term from the initialization. Extensions introduce separate recurrence
equations for trend and seasonality.
