Assessing point forecast accuracy by stochastic error distance

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, and we show that all such loss functions can be written as weighted SEDs. The leading case is absolute error loss. Among other things, this suggests shifting attention away from conditional-mean forecasts and toward conditional-median forecasts.