A new bivariate INAR(1) model with paired Poisson-weighted exponential distributed innovations

Abstract

This paper proposes a novel Bivariate integer-valued auto-regressive model of order 1 with paired Poisson Weighted Exponential (PWE) distributed innovations which is denoted by INAR(1)-PWE with two Sarmanov and classical versions. The CML and CLS estimators of the parameters are obtained and the performance of the proposed models are assessed through some Monte Carlo simulation experiments. Also, the BINAR(1)-PWE is applied to the two real data sets and is compared with some bivariate INAR processes. The research findings commend the BINAR(1)-PWE as another suitable alternative to analyze bivariate series of counts and open the avenues to explore the Sarmanov-based bivariate models.