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Testing exchangeability of copulas in arbitrary dimension

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  • Michael Harder
  • Ulrich Stadtmüller

Abstract

A test for exchangeability of copulas for arbitrary dimensions is proposed, generalising and extending a result by Genest et al. [(2012), ‘Tests of Symmetry for Bivariate Copulas’, Annals of the Institute of Statistical Mathematics, 64, 811–834]. Three test statistics together with some modifications are presented and their asymptotical behaviour is analysed. Empirical p-values are computed by using a bootstrap-procedure proposed by Rémillard and Scaillet [(2009), ‘Testing for Equality between Two Copulas’, Journal of Multivariate Analysis, 100, 377–386] and suggested by Bücher and Dette [(2010), ‘A Note on Bootstrap Approximations for the Empirical Copula Process’, Statistics & Probability Letters, 80, 1925–1932], based on a multiplier central limit theorem by van der Vaart and Wellner [(1996), Weak Convergence and Empirical Processes, Springer Series in Statistics, New York: Springer]. Finally a simulation study compares various versions of the proposed tests.

Suggested Citation

  • Michael Harder & Ulrich Stadtmüller, 2017. "Testing exchangeability of copulas in arbitrary dimension," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 40-60, January.
    • Handle: RePEc:taf:gnstxx:v:29:y:2017:i:1:p:40-60
    DOI: 10.1080/10485252.2016.1253841
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    Cited by:

    1. Beare, Brendan K. & Seo, Juwon, 2020. "Randomization Tests Of Copula Symmetry," Econometric Theory, Cambridge University Press, vol. 36(6), pages 1025-1063, December.
    2. Tarik Bahraoui & Jean‐François Quessy, 2022. "Tests of multivariate copula exchangeability based on Lévy measures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1215-1243, September.
    3. Quessy Jean-François & Bahraoui Tarik, 2018. "Testing the symmetry of a dependence structure with a characteristic function," Dependence Modeling, De Gruyter, vol. 6(1), pages 331-355, December.
    4. Quessy, Jean-François, 2021. "A Szekely–Rizzo inequality for testing general copula homogeneity hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 186(C).

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