A Mixed Thinning Based Geometric INAR(1) Model

Abstract

In this article geometrically distributed integer-valued autoregressive model of order one based on the mixed

thinning operator is introduced. This new thinning operator is defined as a probability mixture of two well

known thinning operators, binomial and negative binomial thinning. Some model properties are discussed.

Method of moments and the conditional least squares are considered as possible approaches in model pa-

rameter estimation. Asymptotic characterization of the obtained parameter estimators is presented. The

adequacy of the introduced model is verified by its application on a certain kind of real-life counting data,

while its performance is evaluated by comparison with two other INAR(1) models that can be also used

over the observed data.