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Estimating ARMAX systems for multivariate time series using the state approach to subspace algorithms

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  • Bauer, Dietmar

Abstract

This paper discusses the asymptotic properties of estimators of ARMAX systems under weak low-level assumptions on the joint input/output process. The prime representative of this class of algorithms is CVA [W.E. Larimore, System identification, reduced order filters and modeling via canonical variate analysis, in: H.S. Rao, P. Dorato (Eds.), Proc. 1983 Amer. Control Conference 2, Piscataway, NJ, 1983, pp. 445-451]. Sufficient assumptions for strong consistency of the transfer function estimators under the assumption of correct specification are derived and explicit bounds on the orders of convergence are given. The assumptions used on the exogenous inputs are considerably weaker than the ones used in the results available in the literature typically requiring the inputs to be ARMA processes themselves, such as is assumed e.g. in [K. Peternell, W. Scherrer, M. Deistler, Statistical analysis of novel subspace identification methods, Signal Processing 52 (1996) 161-177]. Further sufficient conditions for the asymptotic normality of the estimated parameters are given, again under the assumption of correct specification. Finally two order estimation methods are analyzed and conditions for their consistency are derived.

Suggested Citation

  • Bauer, Dietmar, 2009. "Estimating ARMAX systems for multivariate time series using the state approach to subspace algorithms," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 397-421, March.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:3:p:397-421
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    1. Kuersteiner, Guido M., 2005. "Automatic Inference For Infinite Order Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 21(1), pages 85-115, February.
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    3. Bauer, Dietmar, 2005. "Estimating Linear Dynamical Systems Using Subspace Methods," Econometric Theory, Cambridge University Press, vol. 21(1), pages 181-211, February.
    4. Silvia Gonçalves & Lutz Kilian, 2003. "Asymptotic and Bootstrap Inference for AR( Infinite ) Processes with Conditional Heteroskedasticity," CIRANO Working Papers 2003s-28, CIRANO.
    5. Dietmar Bauer, 2005. "Comparing the CCA Subspace Method to Pseudo Maximum Likelihood Methods in the case of No Exogenous Inputs," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(5), pages 631-668, September.
    6. Camba-Méndez, Gonzalo & Kapetanios, George, 2001. "Testing the rank of the Hankel matrix: a statistical approach," Working Paper Series 45, European Central Bank.
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