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Characterization of Differentiable Copulas

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  • Saikat Mukherjee
  • Farhad Jafari
  • Jong-Min Kim
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    Abstract

    This paper proposes a new class of copulas which characterize the set of all twice continuously differentiable copulas. We show that our proposed new class of copulas is a new generalized copula family that include not only asymmetric copulas but also all smooth copula families available in the current literature. Spearman's rho and Kendall's tau for our new Fourier copulas which are asymmetric are introduced. Furthermore, an approximation method is discussed in order to optimize Spearman's rho and the corresponding Kendall's tau.

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    File URL: http://arxiv.org/pdf/1210.2953
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1210.2953.

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    Date of creation: Oct 2012
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    Handle: RePEc:arx:papers:1210.2953

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    Web page: http://arxiv.org/

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    1. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 99(10), pages 2234-2250, November.
    2. Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2004. "A new class of bivariate copulas," Statistics & Probability Letters, Elsevier, Elsevier, vol. 66(3), pages 315-325, February.
    3. Cécile Amblard & Stéphane Girard, 2009. "A new extension of bivariate FGM copulas," Metrika, Springer, Springer, vol. 70(1), pages 1-17, June.
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