Prediction Intervals for Time-Series Forecasting

Abstract

Computing prediction intervals (P.I.s) is an important part of the forecasting process intended to indicate the likely uncertainty in point forecasts. The commonest method of calculating P.I. s i s to use theoretical formulae conditional on a best-fitting model. If a normality assumption is used, it needs to be checked. Alternative computational procedures that are not so dependen t o n a fitted model include the use of empirically based and resampling methods. Some so- called approximate formulae should be avoided. P.I.s tend to be too narrow because out-of - s ample forecast accuracy is often poorer than would be expected from within-sample fit, particularly for P.I.s calculated conditional on a model fitted to past data. Reasons for this i nclude uncertainty about the model and a changing environment. Ways of overcoming these problems include using a mixture of models with a Bayesian approach and using a forecasting m ethod that is designed to be robust to changes in the underlying model. Keywords: