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On the identification and estimation of nonstationary and cointegrated ARMAX systems

Poskitt, D.S. (2006) On the identification and estimation of nonstationary and cointegrated ARMAX systems. Econometric Theory, 22 (6). pp. 1138-1175. ISSN 0266-4666

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Abstract

This paper extends current theory on the identification and estimation of vector time series models to nonstationary processes. It examines the structure of dynamic simultaneous equations systems or ARMAX processes that start from a given set of initial conditions and evolve over a given, possibly infinite, future time horizon. The analysis proceeds by deriving the echelon canonical form for such processes. The results are obtained by amalgamating ideas from the theory of stochastic difference equations with adaptations of the Kronecker index theory of dynamic systems. An extension of these results to the analysis of unit-root, partially nonstationary (cointegrated) time series models is also presented, leading to straightforward identification conditions for the error correction, echelon canonical form. An innovations algorithm for the evaluation of the exact Gaussian likelihood is given. The asymptotic properties of the approximate Gaussian estimator and the exact maximum likelihood estimator based upon the algorithm are derived for the cointegrated case. Examples illustrating the theory are discussed, and some experimental evidence is also presented.

Item Type: Article
Academic Units: The University of York > Economics and Related Studies (York)
Depositing User: York RAE Import
Date Deposited: 05 Jun 2009 13:27
Last Modified: 05 Jun 2009 13:27
Published Version: http://dx.doi.org/10.1017/S0266466606060543
Status: Published
Publisher: Cambridge University Press
Identification Number: 10.1017/S0266466606060543
URI: http://eprints.whiterose.ac.uk/id/eprint/6024

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