Improved estimation for Poisson INAR(1) models

Abstract

We consider the first-order Poisson autoregressive model proposed by McKenzie [Some simple models for discrete variate time series. Water Resour Bull. 1985;21:645–650] and Al-Osh and Alzaid [First-order integer valued autoregressive (INAR(1)) process. J Time Ser Anal. 1987;8:261–275], which may be suitable in situations where the time series data are non-negative and integer valued. We derive the second-order bias of the squared difference estimator [Weiß. Process capability analysis for serially dependent processes of Poisson counts. J Stat Comput Simul. 2012;82:383–404] for one of the parameters and show that this bias can be used to define a bias-reduced estimator. The behaviour of a modified conditional least-squares estimator is also studied. Furthermore, we access the asymptotic properties of the estimators here discussed. We present numerical evidence, based upon Monte Carlo simulation studies, showing that the here proposed bias-adjusted estimator outperforms the other estimators in small samples. We also present an application to a real data set.

Keywords:

• bias correction
• conditional least-squares estimator
• conditional maximum likelihood estimator
• Poisson INAR(1) process
• squared difference estimator

AMS Subject Classification:

• 62F12
• 62M10

Additional information

Funding

The financial supports from the Brazilian governmental institutions CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) [grant number 306700/2009-3] and CAPES (Coordenação de Aperfeiçoamento de Pessoal de Ensino Superior) are here gratefully acknowledged.