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The behavior of a generalized random environment integer-valuedautoregressive model of higher order with geometric marginal distribution {andnegative binomial thinning operator} (abbrev. $RrNGINAR(\mathcal{M,A,P})$) isdictated by a realization $\{z_n\}_{n=1}^\infty$ of an auxiliary Markov chaincalled random environment process. Element $z_n$ represents a state of theenvironment in moment $n\in\mathbb{N}$ and determines three differentparameters of the model in that moment. In order to use$RrNGINAR(\mathcal{M,A,P})$ model, one first needs to estimate$\{z_n\}_{n=1}^\infty$, which was so far done by K-means data clustering. Weargue that this approach ignores some information and performs poorly incertain situations. We propose a new method for estimating$\{z_n\}_{n=1}^\infty$, which includes the data transformation preceding theclustering, in order to reduce the information loss. To confirm its efficiency,we compare this new approach with the usual one when applied on the simulatedand the real-life data, and notice all the benefits obtained from our method.

On Generalized Random Environment INAR Models of Higher Order: Estimation of Random Environment States