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Some results on weak and strong tail dependence coefficients for means of copulas

Author

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  • Fischer, Matthias J.
  • Klein, Ingo

Abstract

Copulas represent the dependence structure of multivariate distributions in a natural way. In order to generate new copulas from given ones, several proposals found its way into statistical literature. One simple approach is to consider convex-combinations (i.e. weighted arithmetic means) of two or more copulas. Similarly, one might consider weighted geometric means. Consider, for instance, the Spearman copula, defined as the geometric mean of the maximum and the independence copula. In general, it is not known whether weighted geometric means of copulas produce copulas, again. However, applying a recent result of Liebscher (2006), we show that every weighted geometric mean of extreme-value copulas produces again an extreme-value copula. The second contribution of this paper is to calculate extremal dependence measures (e.g. weak and strong tail dependence coe±cients) for (weighted) geometric and arithmetic means of two copulas.

Suggested Citation

  • Fischer, Matthias J. & Klein, Ingo, 2007. "Some results on weak and strong tail dependence coefficients for means of copulas," Discussion Papers 78/2007, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    • Handle: RePEc:zbw:faucse:782007
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    Citations

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    Cited by:

    1. László Márkus & Ashish Kumar, 2021. "Modelling Joint Behaviour of Asset Prices Using Stochastic Correlation," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 341-354, March.
    2. Su, Jianxi & Furman, Edward, 2017. "Multiple risk factor dependence structures: Copulas and related properties," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 109-121.
    3. Klein, Ingo & Fischer, Matthias J. & Pleier, Thomas, 2011. "Weighted power mean copulas: Theory and application," FAU Discussion Papers in Economics 01/2011, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics, revised 2011.
    4. Jianxi Su & Edward Furman, 2016. "Multiple risk factor dependence structures: Copulas and related properties," Papers 1610.02126, arXiv.org.
    5. Edward Furman & Jianxi Su & Riv{c}ardas Zitikis, 2014. "Paths and indices of maximal tail dependence," Papers 1405.1326, arXiv.org, revised Jul 2016.

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