Copula structure analysis

Authors: Klüppelberg, Claudia; Kuhn, Gabriel

Source: Journal of the Royal Statistical Society: Series B (Statistical Methodology), Volume 71, Number 3, June 2009 , pp. 737-753(17)

Publisher: Wiley-Blackwell

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Abstract:

Summary.

We extend the standard approach of correlation structure analysis for dimension reduction of high dimensional 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 copulas a correlation-like structure remains, but different margins and non-existence of moments are possible. After introducing the new concept and deriving some theoretical results we observe in a simulation study the performance of the estimators: the theoretical asymptotic behaviour of the statistics can be observed even for small sample sizes. Finally, we show our method at work for a financial data set and explain differences between our copula-based approach and the classical approach. Our new method yielear models also.

Keywords: Copula structure analysis; Correlation structure analysis; Covariance structure analysis; Dimension reduction; Elliptical copula; Factor analysis; Kendall's τ

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9868.2009.00707.x

Affiliations: 1: Technische Universität München, Garching, Germany

Publication date: 2009-06-01