Evaluating Density Forecasts via the Copula Approach

In this paper, we develop parametric tests for the correct density forecasts. Similar to Berkowitz (2001), we construct our tests by nesting a series of i.i.d. uniform random variables in a class of stationary Markov processes. Unlike Berkowitz (2001), the class of Markov processes in this paper is constructed via the copula approach, which allows the separate modeling of the marginal distribution and the temporal dependence of the process. By coupling di®erent marginal distributions with a given copula, our tests have power against alternative processes that exhibit a large variety of marginal properties such as skewed and fat-tailed distributions. Alternatively by coupling a given marginal distribution with di®erent copulas, we obtain tests that have power against alternative processes that exhibit numerous dependence properties such as asymmetric dependence, positive tail dependence, etc. By leaving the marginal distribution unspeci ̄ed, we develop tests for serial independence that are robust to possible misspeci ̄cation of the marginal distribution.