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VAR Cointegration in VARMA Models

Author

Listed:
  • Wagner, Martin

    (Department of Economics, Institute for Advanced Studies)

Abstract

The method for estimation and testing for cointegration put forward by Johansen assumes that the data are described by a vector autoregressive process. In this article we extend the data generating process to autoregressive moving average models without unit roots in the MA polynomial. We first extend some matrix algebraic relationships for I(1) processes and derive their implications for the structure theory of cointegration. Specifically we show that the cointegrating space is invariant to MA errors which have no unit roots in the MA polynomial. The above results permit to prove the robustness of the Johansen estimates of the cointegrating space in a Gaussian vector autoregressive framework when the true model is vector autoregressive moving average, without unit roots in the MA polynomial. The small sample properties of the theoretical results are examined through a small simulation study.

Suggested Citation

  • Wagner, Martin, 1999. "VAR Cointegration in VARMA Models," Economics Series 65, Institute for Advanced Studies.
  • Handle: RePEc:ihs:ihsesp:65
    as

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    File URL: http://www.ihs.ac.at/publications/eco/es-65.pdf
    File Function: First version, 1999
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    References listed on IDEAS

    as
    1. Toda, Hiro Y., 1995. "Finite Sample Performance of Likelihood Ratio Tests for Cointegrating Ranks in Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1015-1032, October.
    2. Bierens, Herman J., 1997. "Nonparametric cointegration analysis," Journal of Econometrics, Elsevier, vol. 77(2), pages 379-404, April.
    3. Ronald Bewley & Minxian Yang, 1998. "On The Size And Power Of System Tests For Cointegration," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 675-679, November.
    4. Haldrup, Niels & Salmon, Mark, 1998. "Representations of I(2) cointegrated systems using the Smith-McMillan form," Journal of Econometrics, Elsevier, vol. 84(2), pages 303-325, June.
    5. Podivinsky, Jan M., 1998. "Testing misspecified cointegrating relationships," Economics Letters, Elsevier, vol. 60(1), pages 1-9, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Segismundo Izquierdo & Ces�reo Hern�ndez & Javier Pajares, 2005. "State Space Modelling of Cointegrated Systems using Subspace Algorithms," Econometrics 0509010, EconWPA, revised 07 Feb 2006.
    2. Martin Wagner, 2004. "A Comparison of Johansen's, Bierens' and the Subspace Algorithm Method for Cointegration Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(3), pages 399-424, July.
    3. Wu, Chung-Shu & Lin, Jin-Lung & Tiao, George C. & Cho, David D., 2005. "Is money demand in Taiwan stable?," Economic Modelling, Elsevier, vol. 22(2), pages 327-346, March.
    4. Bauer, Dietmar & Wagner, Martin, 2002. "Estimating cointegrated systems using subspace algorithms," Journal of Econometrics, Elsevier, vol. 111(1), pages 47-84, November.

    More about this item

    Keywords

    Cointegration; Johansen procedure; Misspecification; Robustness; Simulation; Hausdorff distance;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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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