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Some Results on the Identification and Estimation of Vector ARMAX Processes

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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. Modifications designed to improve the performance of the methods are presented. Some discussion of the practical significance of the results obtained is also provided.

Suggested Citation

  • D.S. Poskitt, 2004. "Some Results on the Identification and Estimation of Vector ARMAX Processes," Monash Econometrics and Business Statistics Working Papers 12/04, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2004-12
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2004/wp12-04.pdf
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    References listed on IDEAS

    as
    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. Lutkepohl, Helmut & Poskitt, D S, 1996. "Specification of Echelon-Form VARMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 69-79, January.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    ARMAX model; consistency; echelon canonical form; efficiency; estimation; identification; Kronecker invariants; least squares; selection criterion; structure determination; subspace algorithm.;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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