An asymptotic total variation test for copulas

TL;DR

This paper introduces a new goodness-of-fit test for copulas using empirical processes and bootstrap methods, which improves power over traditional tests by considering partitions of rectangles, despite the empirical process not converging.

Contribution

It develops a novel asymptotic test for copulas based on empirical copula processes indexed by partitions, with bootstrap p-value estimation despite non-convergence.

Findings

The new test has higher power than the standard Kolmogorov-Smirnov test.

Bootstrap p-values can be consistently estimated despite empirical process non-convergence.

Simulations demonstrate improved performance of the proposed test.

Abstract

We propose a new goodness-of-fit test for copulas, based on empirical copula processes and their nonparametric bootstrap counterparts. The standard Kolmogorov-Smirnov type test for copulas that takes the supremum of the empirical copula process indexed by half spaces is extended by test statistics based on the supremum of the empirical copula process indexed by partitions of Ln rectangles with Ln slowly tending to infinity. Although the underlying empirical process does not converge, it is proved that the p-values of our new test statistic can be consistently estimated by the bootstrap. Simulations confirm that the power of the new procedure is higher than the power of the standard Kolmogorov-Smirnov test for copulas.