Point Forecast Accuracy Evaluation

Here's a new one for your reading pleasure. Interesting history. Minchul and I went in trying to escape the expected loss minimization paradigm. We came out realizing that we hadn't escaped, but simultaneously, that not all loss functions are created equal. In particular, there's a direct and natural connection between our stochastic error divergence (SED) and absolute-error loss, elevating the status of absolute-error loss in our minds and perhaps now making it our default benchmark of choice. Put differently, "quadratic loss is for squares." (Thanks to Roger Koenker for the cute mantra.)

Diebold, F.X. and Shin, M. (2014), "Assessing Point Forecast Accuracy by Stochastic Divergence from Zero," PIER Working Paper 14-011, Department of Economics, University of Pennsylvania.

Abstract: We propose point forecast accuracy measures based directly on the divergence of the forecast-error c.d.f. F(e) from the unit step function at 0, and we explore several variations on the basic theme. We also provide a precise characterization of the relationship between our approach of stochastic error divergence (SED) minimization and the conventional approach of expected loss minimization. The results reveal a particularly strong connection between SED and absolute-error loss and generalizations such as the ``check function" loss that underlies quantile regression.