A Consistent Test for Multivariate Conditional Distributions

We propose a new test for a multivariate parametric conditional distribution of a vector of variables yt given a conditional vector xt. The proposed test is shown to have an asymptotic normal distribution under the null hypothesis, while being consistent for all fixed alternatives, and having non-trivial power against a sequence of local alternatives. Monte Carlo simulations show that our test has reasonable size and good power for both univariate and multivariate models, even for highly persistent dependent data with sample sizes often encountered in empirical finance.