Fast large-sample goodness-of-fit tests for copulas

Abstract

Goodness-of-fit tests are a fundamental element in the copula-based mod- eling of multivariate continuous distributions. Among the different procedures pro- posed in the literature, recent large scale simulations suggest that one of the most powerful tests is based on the empirical process comparing the empirical copula with a parametric estimate of the copula derived under the null hypothesis. As for most of the currently available goodness-of-fit procedures for copula models, the null distribution of the statistic for the latter test is obtained by means of a parametric bootstrap. The main inconvenience of this approach is its high compu- tational cost, which, as the sample size increases, can be regarded as an obstacle to its application. In this work, fast large-sample tests for assessing goodness of fit are obtained by means of multiplier central limit theorems. The resulting procedures are shown to be asymptotically valid when based on popular method-of-moment estimators. Large scale Monte Carlo experiments, involving six frequently used parametric copula families and three different estimators of the copula parameter, confirm that the proposed procedures provide a valid, much faster alternative to the corresponding parametric bootstrap-based tests. An application of the derived tests to the modeling of a well-known insurance data set is presented. The use of the multiplier approach instead of the parametric bootstrap can reduce the computing time from about a day to minutes.