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

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.

Keywords:

• Bivariate integer-valued autoregressive models
• Bivariate negative binomial distribution
• Random coefficient models
• Time series of counts

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Social Science Planning Foundation of Liaoning Province (No. L22ZD065), National Natural Science Foundation of China (Nos. 12271231, 12001229, 11901053) and China Scholarship Council (Grant No. CSC202206170056).