RANDOM ENVIRONMENT INAR MODELS OF HIGHER ORDER

Two different random environment INAR models of higher order, RrNGINARmax(p) and RrNGINAR(1) (p), are introduced. Both of them are of variable order, which is not a random variable. Each step order is defined using the random environment process. Properties of the defined models are analyzed in parallel. The conditional expectation and variance are calculated. The strongly consistent Yule-Walker estimators are defined and new modified estimators are given. Models are applied to the simulated and the real-life data and the results show benefits of the introduced models.