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Tail dependence for multivariate t -copulas and its monotonicity

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  • Chan, Yin
  • Li, Haijun

Abstract

The tail dependence indexes of a multivariate distribution describe the amount of dependence in the upper right tail or lower left tail of the distribution and can be used to analyse the dependence among extremal random events. This paper examines the tail dependence of multivariate t-distributions whose copulas are not explicitly accessible. The tractable formulas of tail dependence indexes of a multivariate t-distribution are derived in terms of the joint moments of its underlying multivariate normal distribution, and the monotonicity properties of these indexes with respect to the distribution parameters are established. Simulation results are presented to illustrate the results.

Suggested Citation

  • Chan, Yin & Li, Haijun, 2008. "Tail dependence for multivariate t -copulas and its monotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 763-770, April.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:763-770
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    References listed on IDEAS

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    1. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2007. "Selecting copulas for risk management," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2405-2423, August.
    2. Rafael Schmidt, 2002. "Tail dependence for elliptically contoured distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 301-327, May.
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    Cited by:

    1. Li, Haijun & Wu, Peiling, 2013. "Extremal dependence of copulas: A tail density approach," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 99-111.
    2. Otiniano, C.E.G. & Rathie, P.N. & Ozelim, L.C.S.M., 2015. "On the identifiability of finite mixture of Skew-Normal and Skew-t distributions," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 103-108.
    3. Balaev, Alexey, 2014. "The copula based on multivariate t-distribution with vector of degrees of freedom," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 90-110.

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