A non‐stationary bivariate INAR(1) process with a simple cross‐dependence: Estimation with some properties

Abstract

This paper considers modelling of a non-stationary bivariate integer-valued autoregressive process of order 1 (BINAR(1)) where the cross-dependence between the counting series is formed through the relationship of the current series with the previous-lagged count series observations while the pair of innovations is independent and marginally Poisson. In addition, this paper proposes a generalised quasi-likelihood (GQL) estimating equation based on the exact specification of the mean score and the auto-covariance structure. The proposed approach is also compared with other popular techniques such as conditional maximum likelihood (CML), generalised least squares (GLS) and generalised method of moment (GMM) based on simulated data from the proposed BINAR(1). Moreover, the model is applied to weekly series of day and night road accidents arising in some regions of Mauritius and is compared with other existing BINAR(1) models.