Alternative Tests for Correct Specification of Conditional Predictive Densities

• Authors: Barbara Rossi.
• BSE Working Paper: 110240 | September 15
• Keywords: predictive density , forecast evaluation , probability integral transform , Kolmogorov-Smirnov test , Cramér-von Mises test
• JEL codes: C22, C52, C53
• predictive density
• forecast evaluation
• probability integral transform
• Kolmogorov-Smirnov test
• Cramér-von Mises test

We propose new methods for evaluating predictive densities in an environment where the estimation error of the parameters used to construct the densities is preserved asymptotically under the null hypothesis. The tests offer a simple way to evaluate the correct specification of predictive densities. Monte Carlo simulation results indicate that our tests are well sized and have good power in detecting misspecifications. An empirical application to the Survey of Professional Forecasters and a baseline macroeconomic model shows the usefulness of our methodology.