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Copula structure analysis

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  • Claudia Klüppelberg
  • Gabriel Kuhn

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.

Suggested Citation

  • Claudia Klüppelberg & Gabriel Kuhn, 2009. "Copula structure analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 737-753, June.
    • Handle: RePEc:bla:jorssb:v:71:y:2009:i:3:p:737-753
    DOI: 10.1111/j.1467-9868.2009.00707.x
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    Cited by:

    1. Dong Hwan Oh & Andrew J. Patton, 2017. "Modeling Dependence in High Dimensions With Factor Copulas," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 139-154, January.
    2. Langworthy, Benjamin W. & Stephens, Rebecca L. & Gilmore, John H. & Fine, Jason P., 2021. "Canonical correlation analysis for elliptical copulas," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    3. Segers, Johan & van den Akker, Ramon & Werker, Bas, 2013. "Semiparametric Gaussian copula models: Geometry and efficient rank-based Estimation," LIDAM Discussion Papers ISBA 2013030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Yu, Long & He, Yong & Zhang, Xinsheng, 2019. "Robust factor number specification for large-dimensional elliptical factor model," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    5. Krupskii, Pavel & Joe, Harry, 2013. "Factor copula models for multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 85-101.
    6. Šárka Hudecová & Miroslav Šiman, 2021. "Testing symmetry around a subspace," Statistical Papers, Springer, vol. 62(5), pages 2491-2508, October.
    7. Quessy, Jean-François & Durocher, Martin, 2019. "The class of copulas arising from squared distributions: Properties and inference," Econometrics and Statistics, Elsevier, vol. 12(C), pages 148-166.

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