Random Environment Integer Valued Autoregressive Process
type="main" xml:id="jtsa12161 abs 0001" An r states random environment integer valued autoregressive process of order 1, RrINAR(1) is introduced. Also, a random environment process is separately defined as a selection mechanism of differently parameterized geometric distributions, thus ensuring the non stationary nature of the RrNGINAR(1) model based on the negative binomial thinning. The distributional and correlation properties of this model are discussed, and the k step ahead conditional expectation and variance are derived. Yule Walker estimators of model parameters are presented and their strong consistency is proved. The RrNGINAR(1) model motivation is justified on simulated samples and by its application to specific real life counting data.