Comparing the accuracy of density forecasts from competing models

A rapidly growing literature emphasizes the importance of evaluating the forecast accuracy of empirical models on the basis of density (as opposed to point) forecasting performance. We propose a test statistic for the null hypothesis that two competing models have equal density forecast accuracy. Monte Carlo simulations suggest that the test, which has a known limiting distribution, displays satisfactory size and power properties. The use of the test is illustrated with an application to exchange rate forecasting.