Forecast accuracy is typically measured in terms of a given loss function. However, as a consequence of the use of misspecified models in multiple model comparisons, relative forecast rankings are loss function dependent. This paper addresses this issue by using a novel criterion for forecast evaluation which is based on the entire distribution of forecast errors. We introduce the concepts of general-loss (GL) forecast superiority and convex-loss (CL) forecast superiority, and we establish a mapping between GL (CL) superiority and first (second) order stochastic dominance. This allows us to develop a forecast evaluation procedure based on an out-of-sample generalization of the tests introduced by Linton, Maasoumi and Whang (2005). The asymptotic null distributions of our test statistics are nonstandard, and resampling procedures are used to obtain the critical values. Additionally, the tests are consistent and have nontrivial local power under a sequence of local alternatives. In addition to the stationary case, we outline theory extending our tests to the case of heterogeneity induced by distributional change over time. Monte Carlo simulations suggest that the tests perform reasonably well in finite samples; and an application to exchange rate data indicates that our tests can help identify superior forecasting models, regardless of loss function.
convex loss function empirical processes forecast superiority general loss function