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Testing the symmetry of a dependence structure with a characteristic function

Author

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  • Quessy Jean-François

    (Université du Québec à Trois-Rivières, Trois-Rivières,Quebec, Canada)

  • Bahraoui Tarik

    (University of Sao Paulo,Sao Paulo, Brazil)

Abstract

This paper proposes competing procedures to the tests of symmetry for bivariate copulas of Genest, Nešlehová and Quessy (2012). To this end, the null hypothesis of symmetry is expressed in terms of the copula characteristic function that uniquely determines the copula of a given bivariate population with continuous marginal distributions. Then, test statistics based on L2 weighted distances computed from an empirical version of the copula characteristic function are proposed. Their asymptotic behavior is derived under the null hypothesis as well as under general alternatives. In particular, it is established that these rank statistics behave asymptotically as first-order degenerate V-statistics under the null hypothesis and this large-sample representation is exploited in order to provide suitably adapted multiplier bootstrap versions for the computation of p-values. The simulations that are reported show that the new tests are more powerful than the competing methods based on the empirical copula introduced by Genest, Nešlehová and Quessy (2012).

Suggested Citation

  • 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.
    • Handle: RePEc:vrs:demode:v:6:y:2018:i:1:p:331-355:n:19
    DOI: 10.1515/demo-2018-0019
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    References listed on IDEAS

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    6. Christian Genest & Johanna Nešlehová, 2014. "On tests of radial symmetry for bivariate copulas," Statistical Papers, Springer, vol. 55(4), pages 1107-1119, November.
    7. Quessy, Jean-François & Rivest, Louis-Paul & Toupin, Marie-Hélène, 2016. "On the family of multivariate chi-square copulas," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 40-60.
    8. Tarik Bahraoui & Taoufik Bouezmarni & Jean†François Quessy, 2018. "A Family of Goodness†of†Fit Tests for Copulas Based on Characteristic Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(2), pages 301-323, June.
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