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ON THE IDENTIFICATION AND ESTIMATION OF NONSTATIONARY ANDCOINTEGRATED ARMAX SYSTEMS

Published online by Cambridge University Press:  03 November 2006

D.S. Poskitt
D.S. Poskitt
Affiliation:
Monash University
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Abstract

This paper extends current theory on the identification andestimation of vector time series models to nonstationary processes.It examines the structure of dynamic simultaneous equations systemsor ARMAX processes that start from a given set of initial conditionsand evolve over a given, possibly infinite, future time horizon. Theanalysis proceeds by deriving the echelon canonical form for suchprocesses. The results are obtained by amalgamating ideas from thetheory of stochastic difference equations with adaptations of theKronecker index theory of dynamic systems. An extension of theseresults to the analysis of unit-root, partially nonstationary(cointegrated) time series models is also presented, leading tostraightforward identification conditions for the error correction,echelon canonical form. An innovations algorithm for the evaluationof the exact Gaussian likelihood is given. The asymptotic propertiesof the approximate Gaussian estimator and the exact maximumlikelihood estimator based upon the algorithm are derived for thecointegrated case. Examples illustrating the theory are discussed,and some experimental evidence is also presented.I thank two referees for insightful comments andhelpful suggestions on the content and presentation of thispaper. I am particularly grateful for the correction of errorsin earlier drafts and reference to the work of B. Hanzon.Financial support under ARC grant DP0343811 is gratefullyacknowledged.

Information

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 6 , December 2006 , pp. 1138 - 1175
Copyright
© 2006 Cambridge University Press

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