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How to model multivariate extremes if one must?

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  • Thomas Mikosch

Abstract

In this paper we discuss some approaches to modeling extremely large values in multivariate time series. In particular, we discuss the notion of multivariate regular variation as a key to modeling multivariate heavy‐tailed phenomena. The latter notion has found a variety of applications in queuing theory, stochastic networks, telecommunications, insurance, finance and other areas. We contrast this approach with modeling multivariate extremes by using the multivariate student distribution and copulas.

Suggested Citation

  • Thomas Mikosch, 2005. "How to model multivariate extremes if one must?," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(3), pages 324-338, August.
    • Handle: RePEc:bla:stanee:v:59:y:2005:i:3:p:324-338
    DOI: 10.1111/j.1467-9574.2005.00289.x
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    Cited by:

    1. Balakrishnan, N. & Hashorva, E., 2011. "On Pearson-Kotz Dirichlet distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 948-957, May.
    2. Gonzalo, J. & Olmo, J., 2007. "The impact of heavy tails and comovements in downside-risk diversification," Working Papers 07/02, Department of Economics, City University London.
    3. J. L. Wadsworth & J. A. Tawn & A. C. Davison & D. M. Elton, 2017. "Modelling across extremal dependence classes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 149-175, January.
    4. Balakrishnan, N. & Hashorva, E., 2013. "Scale mixtures of Kotz–Dirichlet distributions," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 48-58.
    5. Hashorva, Enkelejd, 2006. "On the regular variation of elliptical random vectors," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1427-1434, August.

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