A new generalized binomial thinning-based INAR(1) process with Poisson–Lindley innovations

Abstract

This paper considers a new parameterization of the generalized binomial thinning operator that is to be incorporated in a simple ordered integer-valued autoregressive process (INAR(1)) with the Poisson–Lindley innovations. The statistical properties of the resulting INAR(1) process are explored along with the estimation procedures. Monte Carlo simulation experiments are executed to assess the consistency of the estimates under the new INAR(1) process. Finally, the importance of the proposed INAR(1) model is confirmed through the analysis of a real data set.