Goodness-of-Fit Testing for Copulas: A Distribution-Free Approach

TL;DR

This paper introduces a new distribution-free method for goodness-of-fit testing of copulas using an empirical process that converges to a Wiener process, enabling robust and sensitive tests for copula models.

Contribution

It develops a novel empirical process-based approach for distribution-free copula goodness-of-fit testing, with proven sensitivity and practical effectiveness.

Findings

Process converges to a Wiener process under null hypothesis

Method shows excellent finite-sample performance in simulations

Applicable to real data analysis for copula models

Abstract

Consider a random sample from a continuous multivariate distribution function $F$ with copula $C$. In order to test the null hypothesis that $C$ belongs to a certain parametric family, we construct an empirical process on the unit hypercube that converges weakly to a standard Wiener process under the null hypothesis. This process can therefore serve as a `tests generator' for asymptotically distribution-free goodness-of-fit testing of copula families. We also prove maximal sensitivity of this process to contiguous alternatives. Finally, we demonstrate through a Monte Carlo simulation study that our approach has excellent finite-sample performance, and we illustrate its applicability with a data analysis.