Semiparametric forecast intervals



Consider forecasting the economic variable Yt+h with predictors Xt, where h is the forecast horizon. This paper introduces a semiparametric method that generates forecast intervals of Yt+h|Xt from point forecast models. First, the point forecast model is estimated, thereby taking advantage of its predictive power. Then, nonparametric estimation of the conditional distribution function (CDF) of the forecast error conditional on Xt builds the rest of the forecast distribution around the point forecast, from which symmetric and minimum-length forecast intervals for Yt+h|Xt can be constructed. Under mild regularity conditions, asymptotic analysis shows that (1) regardless of the quality of the point forecast model (i.e., it may be misspecified), forecast quantiles are consistent and asymptotically normal; (2) minimum length forecast intervals are consistent. Proposals for bandwidth selection and dimension reduction are made. Three sets of simulations show that for reasonable point forecast models the method has significant advantages over two existing approaches to interval forecasting: one that requires the point forecast model to be correctly specified, and one that is based on fully nonparametric CDF estimate of Yt+h|Xt. An application to exchange rate forecasting is presented. Copyright © 2010 John Wiley & Sons, Ltd.