Functionals of Clusters of Extremes

J.J.J. Segers

Research output: Working paperDiscussion paperOther research output

230 Downloads (Pure)

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

Fingerprint

Extremes
Multivariate Extreme Value Distribution
Exceedance
Mixing Conditions
Stationary Sequences
Domain of Attraction
Limit Distribution
Approximation
Conditional Distribution
Markov chain
Exceed
Random variable
Higher Order
Converge
Arbitrary

Keywords

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

Cite this

Segers, J. J. J. (2003). Functionals of Clusters of Extremes. (CentER Discussion Paper; Vol. 2003-48). Tilburg: Econometrics.
Segers, J.J.J. / Functionals of Clusters of Extremes. Tilburg : Econometrics, 2003. (CentER Discussion Paper).
@techreport{948d700ba9234068b4ad3df2968bd139,
title = "Functionals of Clusters of Extremes",
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.",
keywords = "cluster functional, extermal index, extreme-value distribution, stationary sequence, tail sequence, threshold exceedance",
author = "J.J.J. Segers",
note = "Pagination: 22",
year = "2003",
language = "English",
volume = "2003-48",
series = "CentER Discussion Paper",
publisher = "Econometrics",
type = "WorkingPaper",
institution = "Econometrics",

}

Segers, JJJ 2003 'Functionals of Clusters of Extremes' CentER Discussion Paper, vol. 2003-48, Econometrics, Tilburg.

Functionals of Clusters of Extremes. / Segers, J.J.J.

Tilburg : Econometrics, 2003. (CentER Discussion Paper; Vol. 2003-48).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Functionals of Clusters of Extremes

AU - Segers, J.J.J.

N1 - Pagination: 22

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - cluster functional

KW - extermal index

KW - extreme-value distribution

KW - stationary sequence

KW - tail sequence

KW - threshold exceedance

M3 - Discussion paper

VL - 2003-48

T3 - CentER Discussion Paper

BT - Functionals of Clusters of Extremes

PB - Econometrics

CY - Tilburg

ER -

Segers JJJ. Functionals of Clusters of Extremes. Tilburg: Econometrics. 2003. (CentER Discussion Paper).