The Level-alpha Hybrid SPA Test and Its Application to Stochastic Dominance

Abstract

In comparing multiple forecasting models, Song suggested a statistical test coupling two different tests, one-sided sup-test and complementary test, to robustify power against local alternative hypotheses. However, his test does not satisfy the level constraint in the limit. Accordingly, I suggest the method to modify the hybrid test to satisfy the constraint by incorporating Hansen's re-centering method. The proposed test is pointwise asymptotically level-alpha and pointwise consistent against any fixed alternative hypothesis. I also extend the idea of coupling to be applicable to the stochastic dominance test, and suggest hybrid stochastic dominance test by incorporating Donald and Hsu's method. Monte-Carlo simulation study shows that the hybrid SPA test outperforms existing tests in certain designs while its performance is similar to that of SPA test by Hansen in most cases in finite sample. Meanwhile it seems that coupling does not enhance the power when it comes to stochastic dominance test.