A non‐stationary bivariate INAR(1) process with a simple cross‐dependence: Estimation with some properties. (28th April 2020) - Bakouch, Hassan S.; Sunecher, Y.; Mamode Khan, N.; Jowaheer, V.
Summary: 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. Abstract : The paper proposes a simple bivariate integer‐valued auto‐regressive process of order 1 (BINAR(1)) with Poisson innovations that can model both stationary and non‐stationary counting series. The proposed model has several desirable properties: The marginal moments illustrate over‐dispersion and the inter‐relation is simply formed by relating the current counting series observation with its same and counter series previous‐lagged observation while the innovations of the two series are assumed to be unrelated. The non‐stationarity in the model is accommodated by the introduction of time‐dependent covariates into the marginal mean function of the innovation terms. Thus, the model parameters consists of the vector of regression effects, the serial and cross correlation coefficients. Since the joint conditional likelihood function yields cumbersome expressions that are numerically tedious to evaluate, we suggest to use the generalized quasi‐likelihood approach to estimate the above parameters. Some data examples are provided to illustrate its application.