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VAR Cointegration in VARMA Models

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  • 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.

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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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Bibliographic Info

Paper provided by Institute for Advanced Studies in its series Economics Series with number 65.

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Length: 37 pages
Date of creation: May 1999
Date of revision:
Handle: RePEc:ihs:ihsesp:65

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Related research

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

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References

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  1. 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.
  2. 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.
  3. 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.
  4. Bierens, H.J., 1995. "Nonparametric cointegration analysis," Discussion Paper 1995-123, Tilburg University, Center for Economic Research.
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Cited by:
  1. Dietmar Bauer & Martin Wagner, 2000. "Estimating Cointegrated Systems Using Subspace Algorithms," Econometric Society World Congress 2000 Contributed Papers 0293, Econometric Society.
  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, 07.
  3. 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.
  4. 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.

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