A new integer-valued AR(1) process based on power series thinning operator

TL;DR

This paper introduces a novel INAR(1) model using power series thinning operators with Poisson-Lindley innovations, providing mathematical analysis, parameter estimation methods, and demonstrating its applicability on real datasets.

Contribution

The paper presents the first INAR(1) model based on power series thinning operators with Poisson-Lindley innovations, including estimation methods and real data applications.

Findings

Model effectively captures count data dynamics.

Parameter estimation methods are compared and discussed.

Real data analysis demonstrates the model's potential.

Abstract

In this paper, we introduce the first-order integer-valued autoregressive (INAR(1)) model, with Poisson-Lindley innovations based on power series thinning operator. Some mathematical features of this process are given and estimating the parameters is discussed by three methods; conditional least squares, Yule-Walker equations and conditional maximum likelihood.Then the results are studied for three special cases of power series operators. Finally, some numerical results are presented with a discussion to the obtained results and Four real data sets are used to show the potentially of the new process.