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The extremal index and clustering of high values for derived stationary sequences

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Ishay Weissman  and
Uri Cohen
Ishay Weissman*
Affiliation:
Technion — Israel Institute of Technology
Uri Cohen*
Affiliation:
Technion — Israel Institute of Technology
*
∗Postal address: Faculty of Industrial Engineering and Management, Technion — Israel Institute of Technology, Technion City, Haifa 32000, Israel.
∗Postal address: Faculty of Industrial Engineering and Management, Technion — Israel Institute of Technology, Technion City, Haifa 32000, Israel.
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Abstract

Given a sequence of independent identically distributed random variables, we derive a moving-maximum sequence (with random translations). The extremal index of the derived sequence is computed and the limiting behaviour of clusters of high values is studied. We are then given two or more independent stationary sequences whose extremal indices are known. We derive a new stationary sequence by taking either a pointwise maximum or by a mixture of the original sequences. In each case, we compute the extremal index of the derived sequence.

Keywords

MIXTURESMOVING MAXIMUMPOINTWISE MAXIMUMSTRONG-MIXING

MSC classification

Primary: 60G10: Stationary processes
Secondary: 60G55: Point processes 60F05: Central limit and other weak theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 972 - 981
Copyright
Copyright © Applied Probability Trust 1995 

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