Prediction Intervals for Time-Series Forecasting

Abstract

Computing prediction intervals (PIs) is an important part of the forecasting process intended to indicate the likely uncertainty in point forecasts. The commonest method of calculating PIs is 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 dependent on a fitted model include the use of empirically based and re-sampling methods. Some so-called approximate formulae should be avoided. PIs tend to be too narrow because out-of-sample forecast accuracy is often poorer than would be expected from within-sample fit, particularly for PIs calculated conditional on a model fitted to past data. Reasons for this include 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 method that is designed to be robust to changes in the underlying model.