, Volume 13, Issue 1, pp 1–33

High-level dependence in time series models

  • Vicky Fasen
  • Claudia Klüppelberg
  • Martin Schlather
Open Access

DOI: 10.1007/s10687-009-0084-8

Cite this article as:
Fasen, V., Klüppelberg, C. & Schlather, M. Extremes (2010) 13: 1. doi:10.1007/s10687-009-0084-8


We present several notions of high-level dependence for stochastic processes, which have appeared in the literature. We calculate such measures for discrete and continuous-time models, where we concentrate on time series with heavy-tailed marginals, where extremes are likely to occur in clusters. Such models include linear models and solutions to random recurrence equations; in particular, discrete and continuous-time moving average and (G)ARCH processes. To illustrate our results we present a small simulation study.


ARCH COGARCH Extreme cluster Extreme dependence measure Extremal index Extreme value theory GARCH Linear model Multivariate regular variation Nonlinear model Lévy-driven Ornstein–Uhlenbeck process Random recurrence equation 

AMS 2000 Subject Classifications

60G70 62G32 62M10 
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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Vicky Fasen
    • 1
  • Claudia Klüppelberg
    • 1
  • Martin Schlather
    • 2
  1. 1.Center for Mathematical SciencesTechnische Universität MünchenGarchingGermany
  2. 2.Centre for StatisticsUniversity of GöttingenGöttingenGermany

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