Application of the BINARMA (1,1) Model with NB Innovations on Accident Data

In this paper, we propose a novel non-stationary bivariate integer-valued autoregressive moving average of order one (BINARMA (1,1)) model with the pair of innovations following a joint Negative Binomial (NB) distribution that accommodates different over-dispersion indices. The model parameters are estimated using the conditional maximum likelihood (CML) estimation method based on thinning and convolution properties. Numerical experiments are also conducted to assess the performance of the CML method based on certain combinations of the model parameters. The proposed BINARMA (1,1) model is also applied on some accident data occurring on the motorway in Mauritius by showing the significant effect of the covariates on the number of accidents.