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Nonparametric Identification of Copula Structures

Author

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  • Bo Li
  • Marc G. Genton

Abstract

We propose a unified framework for testing a variety of assumptions commonly made about the structure of copulas, including symmetry, radial symmetry, joint symmetry, associativity and Archimedeanity, and max-stability. Our test is nonparametric and based on the asymptotic distribution of the empirical copula process. We perform simulation experiments to evaluate our test and conclude that our method is reliable and powerful for assessing common assumptions on the structure of copulas, particularly when the sample size is moderately large. We illustrate our testing approach on two datasets.

Suggested Citation

  • Bo Li & Marc G. Genton, 2013. "Nonparametric Identification of Copula Structures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 666-675, June.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:502:p:666-675
    DOI: 10.1080/01621459.2013.787083
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    Citations

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    Cited by:

    1. Monica Billio & Lorenzo Frattarolo & Dominique Guégan, 2022. "High-Dimensional Radial Symmetry of Copula Functions: Multiplier Bootstrap vs. Randomization," Post-Print hal-04085236, HAL.
    2. Adelchi Azzalini & Marc G. Genton, 2015. "Discussion," International Statistical Review, International Statistical Institute, vol. 83(2), pages 198-202, August.
    3. Beare, Brendan K. & Seo, Juwon, 2020. "Randomization Tests Of Copula Symmetry," Econometric Theory, Cambridge University Press, vol. 36(6), pages 1025-1063, December.
    4. Yuichi Goto & Tobias Kley & Ria Van Hecke & Stanislav Volgushev & Holger Dette & Marc Hallin, 2021. "The Integrated Copula Spectrum," Working Papers ECARES 2021-29, ULB -- Universite Libre de Bruxelles.
    5. Miriam Jaser & Aleksey Min, 2021. "On tests for symmetry and radial symmetry of bivariate copulas towards testing for ellipticity," Computational Statistics, Springer, vol. 36(3), pages 1-26, September.
    6. Mangold, Benedikt, 2017. "New concepts of symmetry for copulas," FAU Discussion Papers in Economics 06/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics, revised 2017.
    7. Billio Monica & Frattarolo Lorenzo & Guégan Dominique, 2021. "Multivariate radial symmetry of copula functions: finite sample comparison in the i.i.d case," Dependence Modeling, De Gruyter, vol. 9(1), pages 43-61, January.
    8. Pavel Krupskii, 2017. "Copula-based measures of reflection and permutation asymmetry and statistical tests," Statistical Papers, Springer, vol. 58(4), pages 1165-1187, December.
    9. Gery Geenens & Arthur Charpentier & Davy Paindaveine, 2014. "Probit Transformation for Nonparametric Kernel Estimation of the Copula Density," Working Papers ECARES ECARES 2014-23, ULB -- Universite Libre de Bruxelles.
    10. Dutta, Subhajit & Genton, Marc G., 2014. "A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 82-93.

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