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Some ARMA models for dependent sequences of poisson counts

Published online by Cambridge University Press:  01 July 2016

Ed Mckenzie
Ed Mckenzie*
Affiliation:
University of Strathclyde
*
∗Postal address: Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK.
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Abstract

A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution of n consecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.

Keywords

BINOMIAL THINNINGDISCRETE SELF-DECOMPOSABILITYPOISSON ARMA PROCESSESMULTIVARIATE POISSON DISTRIBUTIONTIME-REVERSIBILITYMULTINOMIAL THINNINGVECTOR AR(1) PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 20 , Issue 4 , December 1988 , pp. 822 - 835
Copyright
Copyright © Applied Probability Trust 1988 

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