Evaluating Density Forecasts via the Copula Approach

In this paper, we develop a general approach for constructing simple tests for the correct density forecasts, or equivalently, for i.i.d. uniformity of appropriately transformed random variables. It is based on nesting a series of i.i.d. uniform random variables into a class of copula-based stationary Markov processes. As such, it can be used to test for i.i.d. uniformity against alternative processes that exhibit a wide variety of marginal properties and temporal dependence properties, including skewed and fat-tailed marginal distributions, asymmetric dependence, and positive tail dependence. In addition, we develop tests for the dependence structure of the forecasting model that are robust to possible misspecification of the marginal distribution.