Predective Density and Conditional Confidence Interval Accuracy Tests

This paper outlines testing procedures for assessing the relative out-of-sample predictive accuracy of multiple conditional distribution models. The tests that are discussed are based on either the comparison of entire conditional distributions or the comparison of predictive confidence intervals. We also briefly survey existing related methods in the area of predictive density evaluation, including methods based on the probability integral transform and the Kullback-Leibler Information Criterion. The procedures proposed in this paper are similar in many ways to Andrews' (1997) conditional Kolmogorov test and to White's (2000) reality check. In particular, a predictive density test is outlined that involves comparing square (approximation) errors associated with models I, i=1,...,n, by constructing weighted averages over U of E[( F_{i}(u