Copula Structure Analysis Based on Robust and Extreme Dependence Measures

Klüppelberg, Claudia und Kuhn, Gabriel (2006): Copula Structure Analysis Based on Robust and Extreme Dependence Measures. Sonderforschungsbereich 386, Discussion Paper 507

Abstract

In this paper we extend the standard approach of correlation structure analysis in order to reduce the dimension of highdimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulae a correlation-like structure remains but different margins and non-existence of moments are possible. Moreover, elliptical copulae allow also for a copula structure analysis of dependence in extremes. After introducing the new concepts and deriving some theoretical results we observe in a simulation study the performance of the estimators: the theoretical asymptotic behavior of the statistics can be observed even for a sample of only 100 observations. Finally, we test our method on real financial data and explain differences between our copula based approach and the classical approach. Our new method yields a considerable dimension reduction also in non-linear models.

• Dokumententyp: Paper
• Fakultät: Mathematik, Informatik und Statistik > Statistik > Sonderforschungsbereich 386 ; Sonderforschungsbereiche > Sonderforschungsbereich 386
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch