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A Wald Test for the Cointegration Rank in Nonstationary Fractional Systems

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  • Avarucci Marco
  • Velasco Carlos

    (METEOR)

Abstract

This paper develops new methods for determining the cointegration rank in a nonstationary fractionally integrated system, extending univariate optimal methods for testing the degree of integration. We propose a simple Wald test based on the singular value decompositionof the unrestricted estimate of the long run multiplier matrix. When the "strength" of the cointegrating relationship is less than 1/2, the test statistic has a standard asymptotic distribution, like Lagrange Multiplier tests exploiting local properties. We consider the behavior of our test under estimation of short run parameters and local alternatives. We compare our procedure with other cointegration tests based on di erent principles and find that the new method has better properties in a range of situations by using information on the alternative obtained through a preliminary estimate of the cointegration strength.

Suggested Citation

  • Avarucci Marco & Velasco Carlos, 2008. "A Wald Test for the Cointegration Rank in Nonstationary Fractional Systems," Research Memorandum 049, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2008049
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    1. repec:eee:econom:v:199:y:2017:i:1:p:49-62 is not listed on IDEAS
    2. Federico Carlini & Katarzyna Lasak, 2014. "On an Estimation Method for an Alternative Fractionally Cointegrated Model," CREATES Research Papers 2014-15, Department of Economics and Business Economics, Aarhus University.
    3. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.
    4. Majid M. Al-Sadoon, 2014. "A general theory of rank testing," Economics Working Papers 1411, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 2015.
    5. Paolo Santucci de Magistris & Federico Carlini, 2014. "On the identification of fractionally cointegrated VAR models with the F(d) condition," CREATES Research Papers 2014-43, Department of Economics and Business Economics, Aarhus University.

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    Economics (Jel: A);

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