Empirical prediction intervals for additive Holt–Winters methods under misspecification

Abstract

Holt–Winters (HW) methods have been widely used by practitioners for the prediction of time series. However, traditional prediction intervals associated with the HW methods are only theoretically justified for a few types of SARIMA processes. In this article, we propose an empirical prediction interval for a general class of prediction procedures containing the HW methods as special cases. We establish the asymptotic validity of the prediction intervals under mild conditions, which allow model misspecification. Simulation experiments and an application to financial time series are provided to illustrate the good performance of the prediction intervals.