Investigating Improvements in the Accuracy of Prediction Intervals for Combinations of Forecasts: A Simulation Study

Despite a considerable literature on the combination of forecasts, there is little guidance regarding the assessment of their uncertainty. Since combining methods do not involve a formal procedure for identifying the underlying data generating model, theoretical variance expressions are not easily derived. We compare the ability of theoretical, empirical and a new nonparametric method to predict points on the forecast error distribution. Three different approaches to combining, i.e. regression, minimum variance and simple averaging, provide the forecasts using data simulated from five different processes. The new procedure is a hybrid of empirical and theoretical methods that applies quantile regression to empirical fit errors to produce forecast error quantile models which are functions of the lead time. Quantile regression was the most successful procedure for the simple average, which is important as this is the most widely-used combining method, and for non-normal predictive distributions.