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A Asymptotic Total Variation Test for Copulas

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  • Jean-David Fermanian

    ()
    (CREST (ENSAE))

  • Dragan Radulovic

    ()
    (Florida Atlantic University)

  • Marten Wegkamp

    ()
    (Cornell University)

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    Abstract

    We propose a new goodness-of-fit test for copulas, based on empirical copula processes and nonparametric bootstrap counterparts. The standard Kolmogorov-Smirnov type test for copulas that takes the supremum of the empirical copula process indexed by orthants is extended by test statistics based on the supremum of the empirical copula process indexed by families of Ln disjoint boxes, with Ln slowly tending to infinity. Although the underlying empirical process does not converge, the critical values of our new test statistic can be consistently estimated by nonparametric bootstrap techniques, under simple or composite null assumptions. Simulations confirm that the power of the new procedure is oftentimes higher than the power of the standard Kolmogorov-Smirnov or the Cramer-von Mises tests for copulas

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    Bibliographic Info

    Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2013-25.

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    Length: 33
    Date of creation: 2013
    Date of revision:
    Handle: RePEc:crs:wpaper:2013-25

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    Related research

    Keywords: Bootstrap; copula; empirical copula process; goodness-of-fit Test; weak Convergence;

    References

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    1. Hvattum, Lars Magnus & Glover, Fred, 2009. "Finding local optima of high-dimensional functions using direct search methods," European Journal of Operational Research, Elsevier, vol. 195(1), pages 31-45, May.
    2. Bruno Rémillard & Olivier Scaillet, 2006. "Testing For Equality Between Two Copulas," Swiss Finance Institute Research Paper Series 07-24, Swiss Finance Institute.
    3. Bücher, Axel & Dette, Holger, 2010. "A note on bootstrap approximations for the empirical copula process," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1925-1932, December.
    4. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    5. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    6. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
    7. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    8. Daniel Berg, 2009. "Copula goodness-of-fit testing: an overview and power comparison," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 675-701.
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