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Testing the rank of the Hankel matrix: a statistical approach

Author

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  • Camba-Méndez, Gonzalo
  • Kapetanios, George

Abstract

The rank of the Hankel matrix, corresponding to a system transfer function, is equal to the order of its minimal state space realization. The computation of the rank of the Hankel matrix is complicated by the fact that its block elements are rarely given exactly but are estimated instead. In this paper, we propose new statistical tests to determine the rank of the Hankel matrix. We also provide a Monte Carlo study on the reliability of these tests compared to existing procedures. JEL Classification: C12, C15, C32

Suggested Citation

  • Camba-Méndez, Gonzalo & Kapetanios, George, 2001. "Testing the rank of the Hankel matrix: a statistical approach," Working Paper Series 45, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:200145
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    File URL: https://www.ecb.europa.eu//pub/pdf/scpwps/ecbwp045.pdf
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    Citations

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    Cited by:

    1. 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.
    2. d’Artis Kancs & Julda Kielyte, 2002. "Migration in the Enlarged European Union: Empirical Evidence for Labour Mobility in the Baltic States," EERI Research Paper Series EERI_RP_2002_04, Economics and Econometrics Research Institute (EERI), Brussels.
    3. George Kapetanios, 2003. "A New Nonparametric Test of Cointegration Rank," Working Papers 482, Queen Mary University of London, School of Economics and Finance.
    4. Gonzalo Camba-Mendez & George Kapetanios, 2002. "Bootstrap Statistical Tests of Rank Determination for System Identification," Working Papers 468, Queen Mary University of London, School of Economics and Finance.
    5. George Kapetanios, 2003. "Determining the Poolability of Individual Series in Panel Datasets," Working Papers 499, Queen Mary University of London, School of Economics and Finance.
    6. George Kapetanios, 2003. "Determining the Stationarity Properties of Individual Series in Panel Datasets," Working Papers 495, Queen Mary University of London, School of Economics and Finance.
    7. Gonzalo Camba-Mendez & George Kapetanios, 2002. "Bootstrap Statistical Tests of Rank Determination for System Identification," Working Papers 468, Queen Mary University of London, School of Economics and Finance.
    8. Zaka Ratsimalahelo, 2003. "Rank Test Based On Matrix Perturbation Theory," Econometrics 0306008, University Library of Munich, Germany.
    9. Gonzalo Camba-Mendez & George Kapetanios, 2005. "Statistical Tests of the Rank of a Matrix and Their Applications in Econometric Modelling," Working Papers 541, Queen Mary University of London, School of Economics and Finance.
    10. Düker, Marie-Christine & Pipiras, Vladas & Sundararajan, Raanju, 2022. "Cotrending: Testing for common deterministic trends in varying means model," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    11. Bauer, Dietmar, 2008. "Using Subspace Methods For Estimating Arma Models For Multivariate Time Series With Conditionally Heteroskedastic Innovations," Econometric Theory, Cambridge University Press, vol. 24(4), pages 1063-1092, August.
    12. Chortareas, Georgios & Kapetanios, George, 2009. "Getting PPP right: Identifying mean-reverting real exchange rates in panels," Journal of Banking & Finance, Elsevier, vol. 33(2), pages 390-404, February.
    13. Chortareas, Georgios & Kapetanios, George, 2009. "Getting PPP right: Identifying mean-reverting real exchange rates in panels," Journal of Banking & Finance, Elsevier, vol. 33(2), pages 390-404, February.
    14. George Kapetanios, 2003. "A New Nonparametric Test of Cointegration Rank," Working Papers 482, Queen Mary University of London, School of Economics and Finance.
    15. Donald, Stephen G. & Fortuna, Natércia & Pipiras, Vladas, 2007. "On Rank Estimation In Symmetric Matrices: The Case Of Indefinite Matrix Estimators," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1217-1232, December.

    More about this item

    Keywords

    Hankel Operator; model reduction; Monte Carlo; Tests of Rank;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • 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

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