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>

This paper contains a survey of results related to quasi-stationary distributions, which arise in the setting of stochastic dynamical systems that eventually evanesce, and which may be useful in describing the long-term behaviour of such systems before evanescence. We are concerned mainly with...

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...

This paper introduces new classes of bivariate time series models being useful to fit count data time series with a finite range of counts. Motivation comes mainly from the comparison of schemes for monitoring tourism demand, stock data, production and environmental processes. All models are...

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...

Processes of serially dependent Poisson counts are commonly observed in real-world applications and can often be modeled by the first-order integer-valued autoregressive (INAR) model. For detecting positive shifts in the mean of a Poisson INAR(1) process, we propose the one-sided s exponentially...