Non-parametric Estimation of Tail Dependence |
| |
Authors: | RAFAEL SCHMIDT ULRICH STADTMÜLLER |
| |
Institution: | Department of Economic and Social Statistics, University of Cologne; Department of Number Theory and Probability Theory, University of Ulm |
| |
Abstract: | Abstract. Dependencies between extreme events (extremal dependencies) are attracting an increasing attention in modern risk management. In practice, the concept of tail dependence represents the current standard to describe the amount of extremal dependence. In theory, multi-variate extreme-value theory turns out to be the natural choice to model the latter dependencies. The present paper embeds tail dependence into the concept of tail copulae which describes the dependence structure in the tail of multivariate distributions but works more generally. Various non-parametric estimators for tail copulae and tail dependence are discussed, and weak convergence, asymptotic normality, and strong consistency of these estimators are shown by means of a functional delta method. Further, weak convergence of a general upper-order rank-statistics for extreme events is investigated and the relationship to tail dependence is provided. A simulation study compares the introduced estimators and two financial data sets were analysed by our methods. |
| |
Keywords: | asymptotic normality copula empirical copula non-parametric estimation strong consistency tail copula tail dependence tail-dependence coefficient |
|
|