Functionals of Clusters of Extremes

J.J.J. Segers

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Abstract

For arbitrary stationary sequences of random variables satisfying a mild mixing condition, distributional approximations are established for functionals of clusters of exceedances over a high threshold.The approximations are in terms of the distribution of the process conditionally on the event that the first variable exceeds the threshold.This conditional distribution is shown to converge to a non-trivial limit if the finite-dimensional distributions of the process are in the domain of attraction of a multivariate extreme-value distribution.In this case, therefore, limit distributions are obtained for functionals of clusters of extremes, thereby generalizing results for higher-order stationary Markov chains by S.Yun (2000), J.Appl.Probab. 37, 29 44.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages22
Volume2003-48
Publication statusPublished - 2003

Publication series

NameCentER Discussion Paper
Volume2003-48

Keywords

  • cluster functional
  • extermal index
  • extreme-value distribution
  • stationary sequence
  • tail sequence
  • threshold exceedance

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