A regularized goodness-of-fit test for copulas

Résumé

The authors propose an Anderson–Darling-type statistic for copula goodness-of-fit testing. They determine the asymptotic distribution of the statistic under the null hypothesis. As this distribution depends on the unknown value of the copula parameter, they call on a multiplier method to compute the p-value of the test. They assess the power of the test through simulations and find that it is generally superior to that of the Cramér–von Mises statistic based on the distance between the empirical copula and a consistent parametric copula estimate under H0.