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Statistical Methods for Fuzzy Data by Reinhard Viertl

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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)tT assumes a component model

Unnumbered Display Equation

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:

(24.5)Numbered Display Equation

(24.6)Numbered Display Equation

(24.7)Numbered Display Equation

Starting values for the recursion from the first p-values of the time series are calculated as follows:

(24.8) Numbered Display Equation

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 ...

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