This paper proposes a simple new model for stationary time series of integer counts. Previous work has focused on thinning methods and classical time series autoregressive moving-average difference equations; in contrast, our methods use a renewal process to generate a correlated sequence of Bernoulli trials. By superpositioning independent copies of such processes, stationary series with binomial, Poisson, geometric or any other discrete marginal distribution can be readily constructed. The model class proposed is parsimonious, non-Markov and readily generates series with either short- or long-memory autocovariances. The model can be fitted with linear prediction techniques for stationary series. As an example, a stationary series with binomial marginal distributions is fitted to the number of rainy days in 210 consecutive weeks at Key West, Florida. Copyright 2009, Oxford University Press.
