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The behavior of multivariate maxima of moving maxima processes

Part of: Stochastic processes Multivariate analysis

Published online by Cambridge University Press:  14 July 2016

Zhengjun Zhang  and
Richard L. Smith
Zhengjun Zhang*
Affiliation:
Washington University
Richard L. Smith*
Affiliation:
University of North Carolina
*
∗ Postal address: Department of Mathematics, Washington University, Saint Louis, MO 63130-4899, USA. Email address: [email protected]
∗∗ Postal address: Department of Statistics, University of North Carolina, Chapel Hill, NC 27599-3260, USA
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Abstract

In the characterization of multivariate extremal indices of multivariate stationary processes, multivariate maxima of moving maxima processes, or M4 processes for short, have been introduced by Smith and Weissman. Central to the introduction of M4 processes is that the extreme observations of multivariate stationary processes may be characterized in terms of a limiting max-stable process under quite general conditions, and that a max-stable process can be arbitrarily closely approximated by an M4 process. In this paper, we derive some additional basic probabilistic properties for a finite class of M4 processes, each of which contains finite-range clustered moving patterns, called signature patterns, when extreme events occur. We use these properties to construct statistical estimation schemes for model parameters.

Keywords

Multivariate extremeextreme value theorymax-stable processmultivariate extremal index

MSC classification

Primary: 60G70: Extreme value theory; extremal processes 62H05: Characterization and structure theory 60G10: Stationary processes 60G52: Stable processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 1113 - 1123
Copyright
Copyright © Applied Probability Trust 2004 

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