PREDICTION INTERVALS FOR MULTIPLICATIVE HOLT-WINTERS

Yar and Chatfield (1990) have proposed a method of constructing prediction intervals for the additive Holt-Winters forecasting procedure and this companion paper extends the results to the multiplicative seasonal case. In contrast to the additive case, it is shown that the width of 'multiplicative' prediction intervals will depend on the time origin of the forecasts and may decrease (near a seasonal trough) as well as increase with lead time. This key result follows from the form of the Holt-Winters updating equations, and applies whatever assumption is made about the error variance, although more self-consistent results are obtained if the (one-step-ahead) error variance is assumed to be proportional to the seasonal effect rather than constant. An example is presented to compare the proposed prediction intervals, calculated under two different error assumptions, with those obtained using an empirical procedure, which effectively assumes additive errors with constant variance, and those obtained with an 'approximate' procedure. Some general recommendations are made. © 1991.