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

Abstract

The behavior of a generalized random environment integer-valued autoregressive model of higher order with geometric marginal distribution and negative binomial thinning operator is dictated by a realization {zn }∞ of an auxiliary Markov chain called random environment process. Elementzn=1 n represents a state of the environment in moment n ∈ N and determines all parameters of the model in that moment. In order to apply the model, one first needs to estimate {zn }∞, which was so far done by K-means data n=1 clustering. We argue that this approach ignores some information and performs poorly in certain situations. We propose a new method for estimating {zn }∞, which includes the data transformation preceding the n=1 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.