Bivariate INAR(1) model under negative binomial innovations with non-homogeneous over-dispersed indices and application

Abstract

This paper introduces a new bivariate integer-valued autoregressive of order (1) (BINAR(1)) model with negative binomial (NB) innovations under non-stationary moments. The purpose of this time series process is mainly to model series that are affected by time-dependent covariate effects and that, in particular, exhibit different levels of over-dispersion which is a phenomenon commonly noticed in many real-life series applications. In this proposed model, the cross-correlation is induced locally by allowing the current counting series observation to relate with the previous-lagged observation of the other series or vice versa while the pair of NB innovations are assumed uncorrelated. The estimation of the regression, over-dispersion and dependence parameters is conducted using a generalized quasi-likelihood (GQL) approach since the specification of the likelihood function, under non-stationarity, is rather difficult to specify in the above situation. Monte-Carlo simulation experiments are executed to assess the quality of the GQL estimators. The model is also applied and compared with other bivariate time series models to some real-life series in Mauritius.

Keywords:

• BINAR(1)
• non-stationary
• over-dispersion
• GQL
• negative binomial

Acknowledgments

This work is also part of my Post-Doctoral Fellowship on ‘The Family of Bivariate Integer-Valued Autoregressive Models’ at the University of Bahia, Brazil. I am thankful to Prof. Paulo Jorge Canas Rodrigues and to the anonymous reviewers for their suggestions.

Disclosure statement

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