Copula structure analysis based on extreme dependence

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 'correlationlike' 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.