SOME AUTOREGRESSIVE MOVING AVERAGE PROCESSES WITH GENERALIZED POISSONMARGINAL DISTRIBUTIONS

Some simple models are introduced which may be used for modelling or g enerating sequences of dependent discrete random variables with genera lized Poisson marginal distribution. Our approach for building these m odels is similar to that of the Poisson ARMA processes considered by A l-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, 82 2-835). The models have the same autocorrelation structure as their co unterparts of standard ARMA models. Various properties, such as joint distribution, time reversibility and regression behavior, for each mod el are investigated.