Comparison of BINAR(1) models with bivariate negative binomial innovations and explanatory variables

The bivariate integer-valued autoregressive model of order 1 (BINAR(1)) is popular in fitting bivariate time series of counts, and the bivariate negative binomial (BNB) distribution can be chosen as its innovation's distribution, which is more flexible than the traditional bivariate Poisson distribution. It is well known that BNB distributions can be constructed in different ways, and these distributions will be reviewed in this paper. Performances of BINAR(1) models based on these BNB distributions with explanatory variables being included in the survival probability are compared. To estimate unknown parameters, the conditional maximum likelihood method is considered and evaluated by Monte Carlo simulations. Two sales counts are used to compare performances of the above models, and some interesting conclusions are also given.

Automated summary

This paper reviews the relationship between the bivariate integer-valued autoregressive model of order 1 (BINAR(1)) and the bivariate negative binomial (BNB) distribution, compares the performances of BINAR(1) models with explanatory variables in the survival probability under different BNB distributions, and evaluates the parameter estimation method using conditional maximum likelihood through Monte Carlo simulations. Sales counts are used for model performance comparison, leading to interesting conclusions.