Forecasting Models and Prediction Intervals for the Multiplicative Holt-winters Method

A new class of models for data showing trend and multiplicative seasonality is presented. The models allow the forecast error variance to depend on the trend and/or the seasonality. It can be shown that each of these models has the same updating equations and forecast functions as the multiplicative Holt-Winters method, regardless of whether the error variation in the model is constant or not. While the point forecasts from the different models are identical, the prediction intervals will, of course, depend on the structure of the error variance and so it is essential to be able to choose the most appropriate form of model. Two methods for making this choice are presented and examined by simulation.