Generalized Random Environment INAR Models of Higher Order

The random environment integer-valued autoregressive models of higher orders introduced by Nastic et al. (J Time Ser Anal 37: 267-287, 2016) are generalized. Generalizations are made by relaxing two assumptions: the assumption about the equality of negative binomial thinning operators and the assumption that the maximal orders are equal for all the process random states. Some statistical properties of the introduced models are derived and discussed. Their unknown parameters are estimated by the Yule-Walker method and the performances of the obtained estimators are checked using simulated data sets. A possible application of the models on the real-life data is discussed at the end of the paper.