Large-sample tests of extreme-value dependence for multivariate copulas

TL;DR

This paper develops large-sample statistical tests to identify extreme-value dependence in multivariate copulas, using empirical copulas and multiplier techniques, validated through simulations and real data applications.

Contribution

It introduces new large-sample tests for extreme-value dependence in multivariate copulas with proven asymptotic validity and extensive finite-sample performance analysis.

Findings

Tests effectively distinguish extreme-value dependence in simulated data.

Proposed methods outperform existing tests in finite samples.

Applications demonstrate usefulness in financial and geological data analysis.

Abstract

Starting from the characterization of extreme-value copulas based on max-stability, large-sample tests of extreme-value dependence for multivariate copulas are studied. The two key ingredients of the proposed tests are the empirical copula of the data and a multiplier technique for obtaining approximate p-values for the derived statistics. The asymptotic validity of the multiplier approach is established, and the finite-sample performance of a large number of candidate test statistics is studied through extensive Monte Carlo experiments for data sets of dimension two to five. In the bivariate case, the rejection rates of the best versions of the tests are compared with those of the test of Ghoudi, Khoudraji and Rivest (1998) recently revisited by Ben Ghorbal, Genest and Neslehova (2009). The proposed procedures are illustrated on bivariate financial data and trivariate geological data.