Author(s)

Louis G. Doray¹, Andrew Luong², El-Halla Najem¹

¹Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Canada.
²école d’Actuariat, Université Laval, Québec, Canada.

Various models have been proposed in the literature to study non-negative integer-valued time series. In this paper, we study estimators for the generalized Poisson autoregressive process of order 1, a model developed by Alzaid and Al-Osh [1]. We compare three estimation methods, the methods of moments, quasi-likelihood and conditional maximum likelihood and study their asymptotic properties. To compare the bias of the estimators in small samples, we perform a simulation study for various parameter values. Using the theory of estimating equations, we obtain expressions for the variance-covariance matrices of those three estimators, and we compare their asymptotic efficiency. Finally, we apply the methods derived in the paper to a real time series.

Discrete Time Series, Autoregressive Process, Moment Estimator, Quasi-Likelihood, Efficiency, Generalized Poisson, Quasi Binomial Distribution

Doray, L. , Luong, A. and Najem, E. (2016) Efficiency of Some Estimators for a Generalized Poisson Autoregressive Process of Order 1. Open Journal of Statistics, 6, 637-650. doi: 10.4236/ojs.2016.64054.