Assessing Point Forecast Accuracy by Stochastic Error Distance

Abstract

We propose point forecast accuracy measures based directly on distance of the forecast-error c.d.f. from the unit step function at 0 (stochastic error distance, or SED). We provide a precise characterization of the relationship between SED and standard predictive loss functions, showing that all such loss functions can be written as weighted SED's. The leading case is absolute-error loss, in which the SED weights are unity, establishing its primacy. Among other things, this suggests shifting attention away from conditional-mean forecasts and toward conditional-median forecasts.