STATIONARY TIME-SERIES MODELS WITH EXPONENTIAL DISPERSION MODEL MARGINS

We consider a class of stationary infinite-order moving average proces ses with margins in the class of infinitely divisible exponential disp ersion models. The processes are constructed by means of the thinning operation of Joe (1996), generalizing the binomial thinning used by Mc Kenzie (1986, 1988) and Al-Osh and Alzaid (1987) for integer-valued ti me series. As a special case we obtain a class of autoregressive movin g average processes that an different from the ARMA models proposed by Joe (1996). The range of possible marginal distributions for the new models is extensive and includes all infinitely divisible distribution s with finite moment generating functions, hereunder many known discre te, continuous and mixed distributions.