Maximum likelihood estimation of higher-order integer-valued autoregressive processes

Ruijun Bu, Brendan McCabe, Kaddour Hadri

Research output: Contribution to journalArticlepeer-review

55 Citations (Scopus)


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) speci?cation with binomial thinning and Poisson innovations, we examine both the asymptotic e?ciency and ?nite 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 justi?ed, there are substantial gains to be had from using ML especially when the thinning parameters are large.
Original languageEnglish
Pages (from-to)973-994
Number of pages22
JournalJournal of Time Series Analysis
Issue number6
Early online date23 Oct 2008
Publication statusPublished - Nov 2008

Bibliographical note

Corrigendum at 10.1111/j.1467-9892.2009.00609.x

The manuscript entitled: Maximum likelihood estimation of higher-order integer-valued autoregressive processes by Ruijun Bu, Brendan McCabe and Kaddour Hadri published in Journal of Time Series Analysis Volume 29, Number 6, pages 973–994 – November 2008 had an incorrect order of author names on the first page. A change in an author a?liation has also been requested. The order of author names and author a?liations should read: By Ruijun Bu, Kaddour Hadri And Brendan McCabe, The University of Liverpool and Queen’s University Belfast

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability


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