On The Identification and Estimation of Partially Nonstationary ARMAX Systems

Donald Poskitt

No 20/04, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

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 and the asymptotic properties of the approximate Gaussian estimator and the exact maximum likelihood estimator based upon the algorithm are derived. Examples illustrating the theory are discussed and some experimental evidence is also presented.

Keywords: ARMAX; partially nonstationary; Kronecker index theory identification. (search for similar items in EconPapers)
JEL-codes: C10 C32 (search for similar items in EconPapers)
Pages: 37 pages
Date: 2004-10
New Economics Papers: this item is included in nep-ecm
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