A new AR(p) model for time series of counts is investigated, the possible marginal distributions of which are those of the DSD family. We determine the autocorrelation structure of the whole model family and analyze two important special cases. A real-data example demonstrates the practical...

We consider the binomial AR(1) model for serially dependent processes of binomial counts. After a review of its definition and known properties, we investigate marginal and serial properties of jumps in such processes. Based on these results, we propose the jumps control chart for monitoring a...

The INARCH(1) model is a simple but practically relevant, two-parameter model for processes of overdispersed counts with an autoregressive serial dependence structure. We derive closed-form expressions for the joint (central) moments and cumulants of the INARCH(1) model up to order 4. These...