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Unit Roots and Cointegrating Matrix Estimation using Subspace Methods

Author

Listed:
  • Alfredo Garcia Hiernaux

    (Universidad Complutense de Madrid, Dpto. de Fundamentos del Análisis Económico II)

  • Miguel Jerez

    () (Universidad Complutense de Madrid, Dpto. de Fundamentos del Análisis Económico II)

  • José Casals

    (Universidad Complutense de Madrid, Dpto. de Fundamentos del Análisis Económico II)

Abstract

We propose a new procedure to detect unit roots based on subspace methods. It has three main original features. First, the same method can be applied to single or multiple time series. Second, it employs a flexible family of information criteria, which loss functions can be adapted to the statistical properties of the data. Last, it does not require the specification of a stochastic process for the series analyzed. Also, we provide a consistent estimator of the cointegrating rank and the cointegrating matrix. Simulation exercises show that the procedure has good finite sample properties. An example illustrates its application to real time series.

Suggested Citation

  • Alfredo Garcia Hiernaux & Miguel Jerez & José Casals, 2005. "Unit Roots and Cointegrating Matrix Estimation using Subspace Methods," Documentos de Trabajo del ICAE 0512, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  • Handle: RePEc:ucm:doicae:0512
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    File URL: http://eprints.ucm.es/7907/1/0512.pdf
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    References listed on IDEAS

    as
    1. Bauer, Dietmar & Wagner, Martin, 2002. "Estimating cointegrated systems using subspace algorithms," Journal of Econometrics, Elsevier, vol. 111(1), pages 47-84, November.
    2. Casals, Jose & Sotoca, Sonia & Jerez, Miguel, 1999. "A fast and stable method to compute the likelihood of time invariant state-space models," Economics Letters, Elsevier, vol. 65(3), pages 329-337, December.
    3. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 473-495.
    4. Poskitt, Don S, 2000. "Strongly Consistent Determination of Cointegrating Rank via Canonical Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 77-90, January.
    5. Abuaf, Niso & Jorion, Philippe, 1990. " Purchasing Power Parity in the Long Run," Journal of Finance, American Finance Association, vol. 45(1), pages 157-174, March.
    6. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
    7. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    8. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    9. H. Lütkepohl & D. S. Poskitt, 1996. "Consistent Estimation of the Number of Cointegration Relations in a Vector Autoregressive Model," SFB 373 Discussion Papers 1996,74, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    10. Renato Flôres & Pierre-Yves Preumont & Ariane Szafarz, 1995. "Multivariate unit root tests," Working Papers CEB 95-001.RS, ULB -- Universite Libre de Bruxelles.
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    More about this item

    Keywords

    State-space models; subspace methods; unit roots; cointegration.;

    JEL classification:

    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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