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...

The compound Poisson INAR(1) model for time series of overdispersed counts is considered. For such CPINAR(1) processes, explicit results are derived for joint moments, for the k-step-ahead distribution as well as for the stationary distribution. It is shown that a CPINAR(1) process is strongly...

type="main" xml:id="jtsa12054-abs-0001" <p>We present an elaboration of the usual binomial AR(1) process on {0,1, … ,N}that allows the thinning probabilities to depend on the current state N only through the ‘density’ n ∕ N, a natural assumption in many real contexts. We derive some...</p>

Integer-valued autoregressive (INAR) time series form a very useful class of processes suitable to model time series of counts. In the common formulation of Du and Li (1991,JTSA), INAR models of order p share the autocorrelation structure with classical autoregressive time series. This fact...

Popular models for time series of count data are integer-valued autoregressive (INAR) models, for which the literature mainly deals with parametric estimation. In this regard, a semiparametric estimation approach is a remarkable exception which allows for estimation of the INAR models without...

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 detection of patterns in categorical time series data is an important task in many fields of science. Several efficient algorithms for finding frequent sequential patterns have been proposed. An online-approach for sequential pattern analysis based on transforming the categorical alphabet to...

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...