Copula structure analysis based on extreme dependence

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 the 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 copula correlation matrix, which is then analysed through classical covariance structure analysis techniques. After introducing the new concepts and deriving some theoretical results we observe in a simulation study the performance of the estimator. Finally, we test our method on real financial data assessing extreme risk dependence.