BINAR(1) negative binomial model for bivariate non-stationary time series with different over-dispersion indices

摘要

The existing stationary bivariate integer-valued autoregressive model of order 1 (BINAR(1)) with correlated Negative Binomial (NB) innovations is capable of modelling stationary count series where the innovation terms of both series have same over-dispersion index. Such BINAR(1) may not be useful to model real-life series that are affected by common time-dependent covariates whereby the two series may display non-stationarity as well as different over-dispersion indices. In this paper, we propose a novel BINAR(1) model with the pair of innovations following a joint NB distribution that accommodates different over-dispersion indices. The estimation of parameters is conducted using generalized quasi-likelihood (GQL) approach that operates in two phases. Monte Carlo simulations are implemented to assess the performance of the proposed GQL under the wide range of combinations of the model parameters. This BINAR(1) model is also applied to analyze the daily series of day and night accident data in some regions of Mauritius.