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Calculating the extremal index for a class of stationary sequences

Published online by Cambridge University Press:  01 July 2016

Michael R. Chernick ,
Tailen Hsing  and
William P. McCormick
Michael R. Chernick*
Affiliation:
Nichols Research Corporation
Tailen Hsing*
Affiliation:
Texas A & M University
William P. McCormick*
Affiliation:
University of Georgia
*
∗Present address: Risk Data Corporation, Two Venture Plaza, Suite 400, Irvine, CA 92718-3331, USA.
∗∗Postal address: Department of Statistics, Texas A & M University, College Station, TX 77843-3143, USA.
∗∗∗Postal address: Department of Statistics, University of Georgia, Athens, GA 30602, USA.
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Abstract

A local mixing condition D(k) is introduced for stationary sequences satisfying Leadbetter's condition D. Under the local mixing condition, the asymptotic distribution of the sample maximum can be calculated with the knowledge of the joint distribution of k consecutive terms. Some examples are given to illustrate the notion.

Keywords

ARMA PROCESSEXTREME VALUEMIXING CONDITION
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 4 , December 1991 , pp. 835 - 850
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

Research supported by NSF Grant 8814006.

References

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