Tail copula estimation for heteroscedastic extremes
Einmahl,John Zhou,Chen
Einmahl,John
Zhou,Chen
Abstract
Consider independent multivariate random vectors that follow the same copula, but where each marginal distribution is allowed to be non-stationary. This non-stationarity is for each marginal governed by a scedasis function that is the same for all marginals. The usual rank-based estimator of the stable tail dependence function, or, when specialized to bivariate random vectors, the corresponding estimator of the tail copula, is shown to be asymptotic normal. Notably, the heteroscedastic marginals do not affect the limiting process. Next, in the bivariate setup, nonparametric tests for testing whether the scedasis functions for both marginals are the same are developed. Detailed simulations show the good performance of the estimator for the tail dependence coefficient as well as that of the new tests. In particular, novel asymptotic confidence intervals for the tail dependence coefficient are presented and their good finite-sample behavior is shown. Finally an application to the S&P500 and Dow Jones indices reveals that their scedasis functions are about equal and that they exhibit strong tail dependence.
Description
Publisher Copyright: © 2024 The Authors
Date
2024-10
Journal Title
Journal ISSN
Volume Title
Publisher
Research Projects
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Journal Issue
Keywords
extreme value statistics, functional limit theorems, non-identical distributions, tail empirical process, tail dependence, C13 - Estimation: General, C14 - Semiparametric and Nonparametric Methods: General, C12 - Hypothesis Testing: General
Citation
Einmahl, J & Zhou, C 2024, 'Tail copula estimation for heteroscedastic extremes', Econometrics and Statistics. https://doi.org/10.1016/j.ecosta.2024.09.004