TITLE:
Efficiency of Some Estimators for a Generalized Poisson Autoregressive Process of Order 1
AUTHORS:
Louis G. Doray, Andrew Luong, El-Halla Najem
KEYWORDS:
Discrete Time Series, Autoregressive Process, Moment Estimator, Quasi-Likelihood, Efficiency, Generalized Poisson, Quasi Binomial Distribution
JOURNAL NAME:
Open Journal of Statistics,
Vol.6 No.4,
August
23,
2016
ABSTRACT: 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.