Some autoregressive moving average processes with generalized Poisson marginal distributions |
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Authors: | A. A. Alzaid and M. A. Al-Osh |
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Affiliation: | (1) Department of Statistics & Operations Research, College of Science, King Saud University, P.O. Box 2455, 11451 Riyadh, Saudi Arabia |
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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. |
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Keywords: | Generalized Poisson process regression time reversibility quasi-binomial distribution quasi-multinomial distribution vector AR(1) process |
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