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A Family of Goodness†of†Fit Tests for Copulas Based on Characteristic Functions

Author

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  • Tarik Bahraoui
  • Taoufik Bouezmarni
  • Jean†François Quessy

Abstract

A general class of rank statistics based on the characteristic function is introduced for testing goodness†of†fit hypotheses about the copula of a continuous random vector. These statistics are defined as L2 weighted functional distances between a nonparametric estimator and a semi†parametric estimator of the characteristic function associated with a copula. It is shown that these statistics behave asymptotically as degenerate V†statistics of order four and that the limit distributions have representations in terms of weighted sums of independent chi†square variables. The consistency of the tests against general alternatives is established and an asymptotically valid parametric bootstrap is suggested for the computation of the critical values of the tests. The behaviour of the new tests in small and moderate sample sizes is investigated with the help of simulations and compared with a competing test based on the empirical copula. Finally, the methodology is illustrated on a five†dimensional data set.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:45:y:2018:i:2:p:301-323
    DOI: 10.1111/sjos.12300
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    Cited by:

    1. Tarik Bahraoui & Nikolai Kolev, 2021. "New Measure of the Bivariate Asymmetry," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 421-448, February.
    2. Jean-François Quessy, 2021. "On nonparametric tests of multivariate meta-ellipticity," Statistical Papers, Springer, vol. 62(5), pages 2283-2310, October.
    3. Quessy, Jean-François, 2021. "A Szekely–Rizzo inequality for testing general copula homogeneity hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    4. 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.
    5. 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.

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