Parameter space of the Holt-winters' model

Abstract

In the additive Holt-Winters' seasonal exponential smoothing model, it is theoretically possible for smoothing parameters in the usual (0, 1) interval to produce ‘non-invertible’ models. A sample of 406 monthly series reveal that this is a real concern. In the multiplicative model, reasonable estimation procedures produce smoothing constants outside the additive invertible region. When this occurs, the impact on forecasts of values in the distant past is much larger than for recent values and forecasts are poor. Results from the 406 series show that the problem can be avoided and forecasts improved if a subset of the additive invertible region is used as the parameter space.