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Sums and maxima of discrete stationary processes

Part of: Distribution theory Inference from stochastic processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

William P. McCormick  and
Jiayang Sun
William P. McCormick*
Affiliation:
The University of Georgia
Jiayang Sun*
Affiliation:
The University of Michigan
*
∗ Postal address: Department of Statistics, University of Georgia, Athens, GA 30602, USA.
∗∗ Postal address: Department of Statistics, 1444 Mason Hall, The University of Michigan, 419 South State Street, Ann Arbor, MI 48109–1027, USA.
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Abstract

This paper considers the joint limiting behavior of sums and maxima of stationary discrete-valued processes. The asymptotic behavior is a cross between a central limit theorem and asymptotic bounds for the distribution of the maxima. Some applications and simulations are also included.

Keywords

DISCRETE ARMA PROCESSESEXTREME VALUESLIMITING DISTRIBUTIONS

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 62E20: Asymptotic distribution theory 62M10: Time series, auto-correlation, regression, etc.
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 4 , December 1993 , pp. 863 - 876
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Research supported in part by the National Science Foundation under grant DMS-89–02188.

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