Stationary underdispersed INAR(1) models based on the backward approach

TL;DR

This paper develops stationary underdispersed INAR(1) models using the backward approach with Binomial thinning, providing new theoretical insights and specific models demonstrating underdispersion.

Contribution

It introduces new stationary INAR(1) models based on the backward approach with Binomial thinning, focusing on underdispersion and finite mean properties.

Findings

New theoretical results for backward INAR(1) models

Development of underdispersed INAR(1) models

Models with finite mean and underdispersion demonstrated

Abstract

Most of the stationary first-order autoregressive integer-valued (INAR(1)) models were developed for a given thinning operator using either the forward approach or the backward approach. In the forward approach the marginal distribution of the time series is specified and an appropriate distribution for the innovation sequence is sought. Whereas in the backward setting, the roles are reversed. The common distribution of the innovation sequence is specified and the distributional properties of the marginal distribution of the time series are studied. In this article we focus on the backward approach in presence of the Binomial thinning operator. We establish a number of theoretical results which we proceed to use to develop stationary INAR(1) models with finite mean. We illustrate our results by presenting some new INAR(1) models that show underdispersion.