A note on the extremes of a particular moving average count data model

被引：3

作者：

Hall, A ^{[1
]}

Moreira, O ^{[1
]}

机构：

[1] Univ Aveiro, Dept Math, P-3810193 Aveiro, Portugal

来源：

STATISTICS & PROBABILITY LETTERS | 2006年 / 76卷 / 02期

关键词：

extreme value theory; discrete stationary sequences; binomial thinning;

D O I：

10.1016/j.spl.2005.07.002

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this note we present a study of the extremal properties of a particular moving average count data model introduced by McKenzie (1986) [Auto regressive-moving-average processes with negative binomial and geometric marginal distribution. Adv. Appl. Probab. 18, 679-705]. After verifying appropriate dependence conditions, we show that the distribution of the maximum term has the same limiting behaviour as if the sequence was independent and identically distributed. A simulation study illustrates the results. (C) 2005 Published by Elsevier B.V.

引用

页码：135 / 141

页数：7

共 8 条

[1] EXTREME VALUE THEORY FOR A CLASS OF DISCRETE DISTRIBUTIONS WITH APPLICATIONS TO SOME STOCHASTIC PROCESSES [J].

ANDERSON, CW .

JOURNAL OF APPLIED PROBABILITY, 1970, 7 (01) :99-&

[2]

BOX J, 1970, TIME SERIES ANAL

[3]

LAWRANCE AJ, 1980, J ROY STAT SOC B MET, V42, P150

[4]

Leadbetter M. R., 1983, Springer Series in Statistics, DOI 10.1007/978-1-4612-5449-2

[5] ASYMPTOTIC ANALYSIS OF EXTREMES FROM AUTOREGRESSIVE NEGATIVE BINOMIAL PROCESSES [J].

MCCORMICK, WP ;

PARK, YS .

JOURNAL OF APPLIED PROBABILITY, 1992, 29 (04) :904-920

[6] AUTOREGRESSIVE MOVING-AVERAGE PROCESSES WITH NEGATIVE-BINOMIAL AND GEOMETRIC MARGINAL DISTRIBUTIONS [J].

MCKENZIE, E .

ADVANCES IN APPLIED PROBABILITY, 1986, 18 (03) :679-705

[7]

McKenzie E, 2003, HANDB STAT, V21, P573, DOI 10.1016/S0169-7161(03)21018-X

[8] DISCRETE ANALOGS OF SELF-DECOMPOSABILITY AND STABILITY [J].

STEUTEL, FW ;

VANHARN, K .

ANNALS OF PROBABILITY, 1979, 7 (05) :893-899

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