This paper introduces new ways to construct probability integral transforms
of random vectors that complement the approach of Diebold, Hahn, and Tay
(1999) for evaluating multivariate conditional density forecasts. Our approach
enables us to "scan" multivariate densities in various different ways. A simple
bivariate normal example is given that illustrates how "scanning" a multivariate
density from particular angles leads to tests with no power or high power. An
empirical example is also given that applies several different probability integral
transforms to specification testing of Engle's (2002) dynamic conditional correlation
model for multivariate financial returns time series with multivariate
normal and t errors.
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