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Assessing Point Forecast Accuracy by Stochastic Divergence from Zero

We propose and explore several related ways of reducing reliance of point forecast accuracy evaluation on expected loss, E(L(e)), where e is forecast error. Our central approach dispenses with the loss function entirely, instead using a "stochastic error divergence" (SED) accuracy measure based directly on the forecast-error c.d.f., F(e). We explore several variations on the basic theme; interestingly, all point to the primacy of absolute-error loss and its generalizations.