Local asymptotic normality and efficient estimation for multivariate GINAR(p) models

We derive the Local Asymptotic Normality (LAN) property for a multivariate generalized integer-valued autoregressive (MGINAR) process with order p. The generalized thinning operator in the MGINAR(p) process includes not only the usual Binomial thinning but also Poisson thinning, geometric thinning, Negative Binomial thinning and so on. By using the LAN property, we propose an efficient estimation method for the parameter of the MGINAR(p) process. Our procedure is based on the one-step method, which update initial root n-consistent estimators to efficient ones. The one-step method has advantages in both computational simplicity and efficiency. Some numerical results for the asymptotic relative efficiency (ARE) of our estimators and the CLS estimators are presented. In addition, a real data analysis is provided to illustrate the application of the proposed estimation method.