Bootstrap-based Inference for Bivariate Heteroscedastic Extremes with a Changing Tail Copula

TL;DR

This paper develops a bootstrap-based inference framework for bivariate heteroscedastic extremes with changing tail dependence, providing new methods for testing tail index and dependence stability.

Contribution

It introduces a unified, process-centric approach for inference on heteroscedastic extremes with changing tail dependence using bootstrap methods.

Findings

Bootstrap-based tests effectively detect changes in tail dependence.

The asymptotic properties of tail estimators are established.

Simulation results confirm the robustness of the proposed methods.

Abstract

This paper introduces a copula-based model for independent but non-identically distributed data with heteroscedastic extremes marginal and changing tail dependence structures. We establish a unified framework for inference by proving the weak convergence of the bivariate sequential tail empirical process and its empirical bootstrap counterpart. We derive the asymptotic properties of several estimators on the tail, including the quasi-tail copula, integrated scedasis function, and Hill estimator, treating them as functionals of the bivariate sequential tail empirical process. This process-centric approach enables the development of bootstrap-based methods and ensures the theoretical validity of the derived statistics. As an application of our inference method, we propose bootstrap-based tests for the equivalence of extreme value indices, the equivalence of scedasis functions, and non-changing tail dependence when marginal scedasis functions are identical. Our simulations validate the robustness and efficiency of the bootstrap-based tests.