The Poisson distribution is a simple and popular model for count-data random variables, but it suffers from the equidispersion requirement, which is often not met in practice. While models for overdispersed counts have been discussed intensively in the literature, the opposite phenomenon,...

The innovations of an INAR(1) process (<italic>in</italic>teger-valued <italic>a</italic>uto<italic>r</italic>egressive) are usually assumed to be unobservable. There are, however, situations in practice, where also the innovations can be uncovered, i.e. where we are concerned with a <italic>fully observed INAR<roman>(<italic>1</italic>)</roman> process</italic>. We analyze stochastic...

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...