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Rare events, temporal dependence, and the extremal index

Part of: Stochastic processes Nonparametric inference

Published online by Cambridge University Press:  14 July 2016

Johan Segers
Johan Segers*
Affiliation:
Tilburg University
*
∗Postal address: Department of Econometrics and Operations Research, Tilburg University, PO Box 90153, NL-5000 LE Tilburg, The Netherlands. Email address: [email protected]
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Abstract

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Classical extreme value theory for stationary sequences of random variables can to a large extent be paraphrased as the study of exceedances over a high threshold. A special role within the description of the temporal dependence between such exceedances is played by the extremal index. Parts of this theory can be generalized not only to random variables on an arbitrary state space hitting certain failure sets, but even to a triangular array of rare events on an abstract probability space. In the case of M4 (maxima of multivariate moving maxima) processes, the arguments take a simple and direct form.

Keywords

Block maximumexceedanceextremal indexfailure setmixing conditionM4 processrare eventstationary sequence

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 62G32: Statistics of extreme values; tail inference
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 2 , June 2006 , pp. 463 - 485
Copyright
© Applied Probability Trust 2006 

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