Limit Theorems for Extremes in a Particular EARMA (1,1) Sequence.

Abstract

Chernick (1980) showed that when the parameter rho in an EARMA (1, 1) sequence is equal to one, the distribution of the maximum term converges to a distribution of the general form given by Galambos (1978). This distribution is not one of the three extreme-value types. In this report the asymptotic joint distribution of the maximum and minimum is obtained using the same conditioning argument as in Chernick (1980). The maximum and minimum are asymptotically independent and the minimum behaves as if the sequence were a collection of independent and identically distributed random variables even though the maximum does not behave as such. The asymptotic distribution for the range and midrange are also obtained. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 15, 1982
Accession Number
ADA120612

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  • M. R. Chernick

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  • The Aerospace Corporation

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