Bivariate first-order random coefficient integer-valued autoregressive processes based on modified negative binomial operator

TL;DR

This paper introduces a new bivariate integer-valued autoregressive model based on a modified negative binomial operator, with derived properties, estimation methods, and application to crime data.

Contribution

It proposes a novel bivariate RCRI model with dependent innovations and evaluates estimation techniques and forecasting performance.

Findings

Model effectively captures dependence in crime data

Estimation methods show good asymptotic properties

Model outperforms existing alternatives in empirical application

Abstract

In this paper, a new bivariate random coefficient integer-valued autoregressive process based on modified negative binomial operator with dependent innovations is proposed. Basic probabilistic and statistical properties of this model are derived. To estimate unknown parameters, Yule-Walker, conditional least squares and conditional maximum likelihood methods are considered and evaluated by Monte Carlo simulations. Asymptotic properties of the estimators are derived. Moreover, coherent forecasting and possible extension of the proposed model is provided. Finally, the proposed model is applied to the monthly crime datasets and compared with other models.