SOME AUTOREGRESSIVE MOVING AVERAGE PROCESSES WITH GENERALIZED POISSON MARGINAL DISTRIBUTIONS

A. A. ALZAID AND M. A. AL-OSH

Department of Statistics & Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

(Received June 1, 1991; revised January 13, 1992)

Abstract. Some simple models are introduced which may be used for modelling or generating sequences of dependent discrete random variables with generalized Poisson marginal distribution. Our approach for building these models is similar to that of the Poisson ARMA processes considered by Al-Osh and Alzaid (1987, J. Time Ser. Anal., 8, 261–275; 1988, Statist. Hefte, 29, 281–300) and McKenzie (1988, Adv. in Appl. Probab., 20, 822–835). The models have the same autocorrelation structure as their counterparts of standard ARMA models. Various properties, such as joint distribution, time reversibility and regression behavior, for each model are investigated.

Key words and phrases: Generalized Poisson process, regression, time reversibility, quasi-binomial distribution, quasi-multinomial distribution, vector AR(1) process.