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A limit theorem for the maximum term in a particular EARMA(1, 1) sequence

Published online by Cambridge University Press:  14 July 2016

Michael R. Chernick
Michael R. Chernick*
Affiliation:
Oak Ridge National Laboratory
*
∗Postal address: Oak Ridge National Laboratory, Energy Division, POBox X, Oak Ridge, TN 37830, U.S.A.
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Abstract

The EARMA(1, 1) process was described by Jacobs and Lewis (1977). Chernick (1978) showed that the limit for the maximum term is the same as for a sequence of independent, identically distributed exponential random variables when the parameter ρ is less than 1. When ρ = 1, a different limit theorem is obtained. The resulting limit distribution is not an extreme-value type. It is, however, of the general form given by Galambos (1978). The sequence is exchangeable.

Keywords

MAXIMALIMIT THEOREMEXCHANGEABLE SEQUENCES
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 869 - 873
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

Research sponsored by the Energy Information Administration, U.S. Department of Energy, under Contract W-7405-ENG-26 with the Union Carbide Corporation.

References

Chernick, M. R. (1978) Mixing Conditions and Limit Theorems for Maxima of Some Stationary Sequences. Ph.D. Dissertation, Department of Statistics, Stanford University.Google Scholar
Galambos, J. (1978) The Asymptotic Theory of Extreme Order Statistics. Wiley, New York.Google Scholar
Jacobs, P. A. and Lewis, P. A. W. (1977) A mixed autoregressive moving average exponential sequence and point process (EARMA 1, 1). Adv. Appl. Prob. 9, 87–104.Google Scholar
Leadbetter, M. R. (1974) On extreme values in stationary sequences. Z. Wahrscheinlichkeitsth. 28, 289–303.Google Scholar