Prediction intervals for the Holt-Winters forecasting procedure

Abstract

Prediction interval formulae are derived for the Holt-Winters forecasting procedure with an additive seasonal effect. The formulae make no assumptions about the 'true' underlying model. The results are contrasted with those obtained from various alternative approaches to the calculation of prediction intervals. Some large discrepancies are noted and it is suggested that the formulae presented here should be preferred to those which depend on an inappropriate deterministic model or which depend on invalid generalised approximations which take no account of the particular properties of the given series. Results for cumulative forecasts and for a damped trend model are also given. For completeness we also give results for one- and two-parameter exponential smoothing. Finally, we make some general comments as to why prediction intervals tend to be too narrow in practice.