MAXIMUM LIKELIHOOD ESTIMATION OF HIGHER-ORDER INTEGER-VALUED AUTOREGRESSIVE PROCESSES

Bu, Ruijun ORCID: 0000-0002-3947-3038, McCabe, Brendan ORCID: 0000-0002-9731-1766 and Hadri, Kaddour (2008) MAXIMUM LIKELIHOOD ESTIMATION OF HIGHER-ORDER INTEGER-VALUED AUTOREGRESSIVE PROCESSES JOURNAL OF TIME SERIES ANALYSIS, 29 (6). pp. 973-994. ISSN 0143-9782, 1467-9892

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Abstract

In this article, we extend the earlier work of Freeland and McCabe [Journal of time Series Analysis (2004) Vol. 25, pp. 701-722] and develop a general framework for maximum likelihood (ML) analysis of higher-order integer-valued autoregressive processes. Our exposition includes the case where the innovation sequence has a Poisson distribution and the thinning is binomial. A recursive representation of the transition probability of the model is proposed. Based on this transition probability, we derive expressions for the score function and the Fisher information matrix, which form the basis for ML estimation and inference. Similar to the results in Freeland and McCabe (2004), we show that the score function and the Fisher information matrix can be neatly represented as conditional expectations. Using the INAR(2) specification with binomial thinning and Poisson innovations, we examine both the asymptotic efficiency and finite sample properties of the ML estimator in relation to the widely used conditional least squares (CLS) and Yule-Walker (YW) estimators. We conclude that, if the Poisson assumption can be justified, there are substantial gains to be had from using ML especially when the thinning parameters are large. © 2008 The Authors.

Item Type:	Article
Additional Information:	## TULIP Type: Articles/Papers (Journal) ##
Uncontrolled Keywords:	Time series of counts, INAR(p) model, Poisson autoregressive models, maximum likelihood estimation, asymptotic relative efficiency
Depositing User:	Symplectic Admin
Date Deposited:	17 Oct 2016 09:04
Last Modified:	16 Jun 2026 20:14
DOI:	10.1111/j.1467-9892.2008.00590.x
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3003791
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