How to model multivariate extremes if one must?

Authors

  • Thomas Mikosch

    1. Laboratory of Actuarial Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
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      Thomas Mikosch's research is partially supported by MaPhySto, The Danish Research Network for Mathematical Physics and Stochastics, and Dynstoch, a research training network under the programme Improving Human Potential financed by The 5th Framework Programme of the European Commission. Financial support by the Danish Research Council (SNF) Grant No 21-01-0546 is gratefully acknowledged by the author. mikosch@math.ku.dk


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.

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