A Note on the Specification and Estimation of ARMAX Systems

Research output: Contribution to journalArticlepeer-review


  • D.S. Poskitt


Publication details

JournalJournal of Time Series Analysis
DatePublished - 17 Feb 2005
Issue number2
Number of pages26
Pages (from-to)157-183
Original languageEnglish


This paper addresses the problem of identifying echelon canonical forms for a vector autoregressive moving-average model with exogenous variables using finite algorithms. For given values of the Kronecker indices, a method for estimating the structural parameters of a model using ordinary least squares calculations is presented. These procedures give rise, rather naturally, to a technique for the determination of the structural indices based on the use of conventional model selection criteria. A detailed analysis of the statistical properties of the estimation and identification procedures is given and some evidence on the practical significance of the results obtained is also provided. The conclusion briefly discusses modifications designed to improve the performance of the identification method and points to the application of the techniques to subspace algorithms.

    Research areas

  • ARMAX model • consistency • echelon canonical form • efficiency • estimation • identification • Kronecker invariants • least squares • selection criterion • structure determination • subspace algorithm

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