Trends in tail dependence of heteroscedastic extremes

2026-04-13

AI Summary

This study addresses the challenge of simultaneously modeling time-varying tail dependence structures and heteroskedastic marginal distributions in independent but non-identically distributed random vectors. The authors propose a nonparametric method to estimate the integrated tail copula and establish its asymptotic theory. Notably, this work is the first to investigate time-varying tail dependence under heteroskedastic margins, demonstrating that heteroskedasticity does not affect the limiting distribution of the integrated tail copula estimator. This insight enables the construction of an effective statistical test for assessing whether the tail copula remains constant over time. Theoretical analysis confirms the asymptotic efficiency of the proposed estimator, and simulation studies corroborate its strong finite-sample performance and high statistical power.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

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.

Problem

• tail dependence
• heteroscedastic extremes
• tail copula
• nonidentically distributed
• multivariate extreme value

Innovation

• tail copula
• heteroscedastic extremes
• nonparametric estimation
• integrated tail copula
• extreme value statistics