Here we obtain difference equations for the higher order moments and cumulants of a time series {X_t} satisfying an INAR(p) model. These equations are similar to the difference equations for the higher order moments and cumulants of the bilinear time series model. We obtain the spectral and...

This paper presents an initial review of the theoretical and measurement discussions of sustainability and its relation to human development. As we show in this paper, there is an overall consensus about the importance of sustaining development and well-being over time, but in reality different...

Time series of daily mean temperature obtained from the European Climate Assessment data set is analyzed with respect to their extremal properties. A time-series clustering approach which combines Bayesian methodology, extreme value theory and classification techniques is adopted for the...

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>