Goodness-of-fit Test for Specification of Semiparametric Copula Dependence Models

This paper concerns goodness-of-fit test for semiparametric copula models. Our contribution is two-fold: we first propose a new test constructed via the comparison between "in-sample" and "out-of-sample" pseudolikelihoods, which avoids the use of any probability integral transformations. Under the null hypothesis that the copula model is correctly specified, we show that the proposed test statistic converges in probability to a constant equal to the dimension of the parameter space and establish the asymptotic normality for the test. Second, we introduce a hybrid mechanism to combine several test statistics, so that the resulting test will make a desirable test power among the involved tests. This hybrid method is particularly appealing when there exists no single dominant optimal test. We conduct comprehensive simulation experiments to compare the proposed new test and hybrid approach with the best "blank test" shown in Genest et al. (2009). For illustration, we apply the proposed tests to analyze three real datasets.