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The Rank of a Sub-Matrix of Cointegration

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  • Kurozumi, Eiji

Abstract

This paper proposes a test of the rank of the sub-matrix of b, where b is a cointegrating matrix. In addition, the sub-matrix of d, an orthogonal complement to b, is investigated. We show that information on the rank of the sub-matrix of b and/or d is useful in several situations. We construct the test statistic by using the eigenvalues of the quadratic form of the sub-matrix. We show that the test statistic has a limiting chi-squared distribution when the data is non-trending, and we propose a conservative test when the data is trending. Finite sample simulations show that, although the simulation settings are limited, the proposed test works well.

Suggested Citation

  • Kurozumi, Eiji, 2003. "The Rank of a Sub-Matrix of Cointegration," Discussion Papers 2002-15, Graduate School of Economics, Hitotsubashi University.
  • Handle: RePEc:hit:econdp:2002-15
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    1. Joseph P. Newhouse, 1992. "Medical Care Costs: How Much Welfare Loss?," Journal of Economic Perspectives, American Economic Association, vol. 6(3), pages 3-21, Summer.
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    Cited by:

    1. Mauricio, Jose Alberto, 2006. "Exact maximum likelihood estimation of partially nonstationary vector ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3644-3662, August.
    2. Bertocco Giancarlo, 2006. "Are banks special? A note on Tobin’s theory of financial intermediaries," Economics and Quantitative Methods qf0605, Department of Economics, University of Insubria.
    3. Paolo Paruolo, 2006. "The Likelihood Ratio Test for the Rank of a Cointegration Submatrix," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 921-948, December.
    4. Gomez-Biscarri, Javier & Hualde, Javier, 2015. "Regression-based analysis of cointegration systems," Journal of Econometrics, Elsevier, pages 32-50.

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