Statistics and Its Interface

Volume 8 (2015)

Number 1

Special Issue on Extreme Theory and Application (Part II)

Guest Editors: Yazhen Wang and Zhengjun Zhang

Copula structure analysis based on extreme dependence

Pages: 93 – 107

DOI: https://dx.doi.org/10.4310/SII.2015.v8.n1.a9

Authors

Claudia Klüppelberg (Zentrum Mathematik, Technische Universität München, Garching, Germany)

Stephan Haug (Zentrum Mathematik, Technische Universität München, Garching, Germany)

Gabriel Kuhn (Zentrum Mathematik, Technische Universität München, Garching, Germany)

Abstract

We introduce a technique to analyse the dependence structure of an elliptical copula with focus on extreme observations. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of an elliptical copula in the high risk observations. More precisely, we describe the extreme dependence structure by an elliptical copula, which preserves a ‘correlation-like’ structure in the extremes. Based on the tail dependence function we estimate the extreme copula correlation matrix, which is then analysed through classical covariance structure analysis techniques. After introducing the new concepts we derive some theoretical results. A simulation study shows that the estimator performs very well even under the complexity of the extreme value problem. Finally, we use our method on real financial data assessing extreme risk dependence.

Keywords

extreme dependence, extreme value statistics, elliptical copula, factor analysis, Kendall’s tau, multivariate statistics, risk analysis, structure analysis, tail dependence function

2010 Mathematics Subject Classification

Primary 62G32, 62H20, 62H25. Secondary 60G70, 62H12.

Published 13 February 2015