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Klüppelberg, Claudia
Kuhn, Gabriel
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Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 507
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.
copula structure analysis
correlation structure analysis
covariance structure analysis
dimension reduction
elliptical copula
factor analysis
Kendall's tau
tail copula
tail dependence
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Working Paper

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