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A Note on the Specification and Estimation of ARMAX Systems

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  • D. S. Poskitt
Abstract
. 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.

Suggested Citation

  • D. S. Poskitt, 2005. "A Note on the Specification and Estimation of ARMAX Systems," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 157-183, March.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:2:p:157-183
    DOI: 10.1111/j.1467-9892.2005.00397.x
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    References listed on IDEAS

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    1. Poskitt, D. S. & Salau, M. O., 1994. "On the Asymptotic Relative Efficiency of Gaussian and Least Squares Estimators for Vector ARMA Models," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 294-317, November.
    2. D. S. Poskitt & A. R. Tremayne, 1986. "Some Aspects Of The Performance Of Diagnostic Checks In Bivariate Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 217-233, May.
    3. Lai, T. L. & Wei, C. Z., 1982. "Asymptotic properties of projections with applications to stochastic regression problems," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 346-370, September.
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    Cited by:

    1. Guy Melard, 2020. "An Indirect Proof for the Asymptotic Properties of VARMA Model Estimators," Working Papers ECARES 2020-10, ULB -- Universite Libre de Bruxelles.
    2. D.S. Poskitt, 2009. "Vector Autoregresive Moving Average Identification for Macroeconomic Modeling: Algorithms and Theory," Monash Econometrics and Business Statistics Working Papers 12/09, Monash University, Department of Econometrics and Business Statistics.
    3. Mélard, Guy, 2022. "An indirect proof for the asymptotic properties of VARMA model estimators," Econometrics and Statistics, Elsevier, vol. 21(C), pages 96-111.
    4. Poskitt, D.S., 2016. "Vector autoregressive moving average identification for macroeconomic modeling: A new methodology," Journal of Econometrics, Elsevier, vol. 192(2), pages 468-484.

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