Trends in tail dependence of heteroscedastic extremes

TL;DR

This paper develops a nonparametric estimator for the integrated tail copula in multivariate heteroscedastic extremes, demonstrating its asymptotic properties and applying it to test for constant tail dependence.

Contribution

It introduces a new estimator for the integrated tail copula under heteroscedasticity and proves its asymptotic behavior, enabling testing of tail dependence consistency.

Findings

Estimator has good finite-sample performance.

Heteroscedastic marginals do not influence the asymptotic limit.

The test for constant tail copula shows high power in simulations.

Abstract

We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly changing tail copulas, we propose a nonparametric estimator for the integrated tail copula and establish its asymptotic behavior. Notably, the heteroscedastic marginals do not affect the limiting processes. We use the main result for the integrated tail copula to test for a constant tail copula across all observations. Finally, a simulation study shows the good finite-sample behavior of our limit theorems as well as high power of the test.