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

Pirkovi'c, Bogdan A.; Laketa, Petra N.; Nasti'c, Aleksandar S.

The behavior of a generalized random environment integer-valued autoregressive model of higher order with geometric marginal distribution {and negative binomial thinning operator} (abbrev. $RrNGINAR(\mathcal{M,A,P})$) is dictated by a realization $\{z_n\}_{n=1}^\infty$ of an auxiliary Markov chain called random environment process. Element $z_n$ represents a state of the environment in moment $n\in\mathbb{N}$ and determines three different parameters 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. We argue that this approach ignores some information and performs poorly in certain situations. We propose a new method for estimating $\{z_n\}_{n=1}^\infty$, which includes the data transformation preceding the clustering, in order to reduce the information loss. To confirm its efficiency, we compare this new approach with the usual one when applied on the simulated and the real-life data, and notice all the benefits obtained from our method.