Maximum Likelihood Estimation of Higher-Order Integer-Valued Autoregressive Processes

22 Pages Posted: 27 Oct 2008

See all articles by Ruijun Bu

Ruijun Bu

University of Liverpool - Management School (ULMS)

Brendan P.M. McCabe

University of Liverpool - Management School (ULMS)

Kaddour Hadri

Durham Business School

Date Written: 0000

Abstract

In this article, we extend the earlier work of Freeland and McCabe [Journal of time Series Analysis (2004) Vol. 25, pp. 70-722] 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 YuleWalker (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.

Suggested Citation

Bu, Ruijun and McCabe, Brendan P.M. and Hadri, Kaddour, Maximum Likelihood Estimation of Higher-Order Integer-Valued Autoregressive Processes (0000). Journal of Time Series Analysis, Vol. 29, Issue 6, pp. 973-994, November 2008, Available at SSRN: https://ssrn.com/abstract=1288876 or http://dx.doi.org/10.1111/j.1467-9892.2008.00590.x

Ruijun Bu (Contact Author)

University of Liverpool - Management School (ULMS) ( email )

Chatham Street
Liverpool, L69 7ZH
United Kingdom

Brendan P.M. McCabe

University of Liverpool - Management School (ULMS) ( email )

Chatham Street
Liverpool, L69 7ZH
United Kingdom

Kaddour Hadri

Durham Business School ( email )

Mill Hill Lane
Durham, Durham DH1 3LB
United Kingdom

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