24.6 Generalized Holt–Winter method
For details of the Holt–Winter method in the case of standard time series see Janacek (2001).
The Holt–Winter method for standard time series (xt)t∈T assumes a component model
with local linear trend mt = a + b t and period length p of the seasonal component st. If for time N − 1 estimators and are given, then the estimates for time N can be calculated recursively:
Starting values for the recursion from the first p-values of the time series are calculated as follows:
The value follows the assumption that at the beginning no trend is present. A h-step prediction at time N, with h > 0, is given by
There are different approaches ...