Random environment integer-valued autoregressive process

Aleksandar S. Nastić, Petra N. Laketa and Miroslav M. Ristić

Journal of Time Series Analysis, 2016, vol. 37, issue 2, 267-287

Abstract: type="main" xml:id="jtsa12161-abs-0001"> An r states random environment integer-valued autoregressive process of order 1, RrINAR(1), is introduced. Also, a random environment process is separately defined as a selection mechanism of differently parameterized geometric distributions, thus ensuring the non-stationary nature of the RrNGINAR(1) model based on the negative binomial thinning. The distributional and correlation properties of this model are discussed, and the k-step-ahead conditional expectation and variance are derived. Yule–Walker estimators of model parameters are presented and their strong consistency is proved. The RrNGINAR(1) model motivation is justified on simulated samples and by its application to specific real-life counting data.

Date: 2016
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