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...

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>

A new and flexible class of ARMA‐like (autoregressive moving average) models for nominal or ordinal time series is proposed, which are characterized by using so‐called weighting operators and are, thus, referred to as weighted discrete ARMA (WDARMA) models. By choosing an appropriate type of...