A Asymptotic Total Variation Test for Copulas

We propose a new goodness-of-fit test for copulas, based on empirical copula processes and nonparametric bootstrap counterparts. The standard Kolmogorov-Smirnov type test for copulas that takes the supremum of the empirical copula process indexed by orthants is extended by test statistics based on the supremum of the empirical copula process indexed by families of Ln disjoint boxes, with Ln slowly tending to infinity. Although the underlying empirical process does not converge, the critical values of our new test statistic can be consistently estimated by nonparametric bootstrap techniques, under simple or composite null assumptions. Simulations confirm that the power of the new procedure is oftentimes higher than the power of the standard Kolmogorov-Smirnov or the Cramer-von Mises tests for copulas