Statistical Inference on a Changing Extremal Dependence Structure

TL;DR

This paper develops estimators and tests for detecting changes in the extremal dependence structure of multivariate regularly varying vectors over time, with proven asymptotic properties and validated through simulations.

Contribution

It introduces new estimators for the spectral measure at specific times and over time, along with tests for temporal stability of the extremal dependence structure.

Findings

Estimators are asymptotically normal under certain conditions.

Tests effectively detect changes in spectral measures in simulations.

Method performs well in finite samples.

Abstract

We analyze the extreme value dependence of independent, not necessarily identically distributed multivariate regularly varying random vectors. More specifically, we propose estimators of the spectral measure locally at some time point and of the spectral measures integrated over time. The uniform asymptotic normality of these estimators is proved under suitable nonparametric smoothness and regularity assumptions. We then use the process convergence of the integrated spectral measure to devise consistent tests for the null hypothesis that the spectral measure does not change over time. The finite sample performance of these tests is investigated in Monte Carlo simulations.