Alternative tests for correct specification of conditional predictive densities

We propose a new framework 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, where both the model specification and its estimation technique are evaluated jointly. Monte Carlo simulation results indicate that our tests are well sized and have good power in detecting misspecification. An empirical application to density forecasts of the Survey of Professional Forecasters shows the usefulness of our methodology.