How to model multivariate extremes if one must?


  • 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.


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.