In this Time Series model, the simple exponential smoothing forecasts are “enhanced” both by an exponential trend component (independently smoothed with parameter g) and an additive seasonal component (smoothed with parameter d). For example, suppose we wanted to forecast the monthly revenue for a resort area. Every year, revenue may increase by a certain percentage or factor, resulting in an exponential trend in overall revenue. In addition, there could be an additive seasonal component, for example a particular fixed (and slowly changing) amount of added revenue during the December holidays.
To compute the smoothed values for the first season, initial values for the seasonal components are necessary. By default, the Time Series module will estimate those values (for all models including a seasonal component) from the data via Classical seasonal decomposition. Also, to compute the smoothed value (forecast) for the first observation in the series, both estimates of S0 and T0 (initial trend) are necessary. By default, these values are computed as:
T0 = exp((log(Mk) - log(M1))/p)
where
k | is the number of complete seasonal cycles |
Mk | is the mean for the last seasonal cycle |
M1 | is the mean for the first seasonal cycle |
p | is the length of the seasonal cycle |
and S0 = exp(log(M1) - p*log(T0)/2)