Common approaches to test for the economic value of directional forecasts are based on the classical Chi-square test for independence, Fisher’s exact test or the Pesaran and Timmerman (1992) test for market timing. These tests are asymptotically valid for serially independent observations....

The technique of using densities and conditional distributions to carry out consistent specification testing and model selection amongst multiple diffusion processes have received considerable attention from both financial theoreticians and empirical econometricians over the last two decades....