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Likelihood Ratio Testing for Cointegration Ranks in I(2) Models


  • Heino Bohn Nielsen

    (University of Copenhagen, Institute of Economics)

  • Anders Rahbek

    (University of Copenhagen, Dept. of Applied Mathematics and Statistsics)


This paper presents the likelihood ratio (LR) test for the number of cointegrating and multi-cointegrating relations in the I(2) vector autoregressive model. It is shown that the asymptotic distribution of the LR test for the (multi-) cointegration ranks is identical to the asymptotic distribution of the much applied test statistic based on the Two-Step procedure in Johansen (1995), Paruolo (1996), and Rahbek, Kongsted, and Jørgensen (1999). By construction the LR test statistic is smaller than the non-LR test statistic from the Two-Step procedure as the latter ignores some of the restrictions concerning the hypothesis of I(2), and application of the LR test may change rank selection in empirical work. Based on a study of existing empirical applications and related Monte Carlo simulations we conclude that the LR test has much better size properties when compared to the Two-Step based test. Overall, we propose to use of the LR test for rank determination in I(2) analysis as the Two-Step based statistic was developed as a feasible approximation to the then unobtainable LR test.

Suggested Citation

  • Heino Bohn Nielsen & Anders Rahbek, 2003. "Likelihood Ratio Testing for Cointegration Ranks in I(2) Models," Discussion Papers 03-42, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:0342

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    References listed on IDEAS

    1. Paruolo, Paolo, 2000. "Asymptotic Efficiency Of The Two Stage Estimator In I (2) Systems," Econometric Theory, Cambridge University Press, vol. 16(4), pages 524-550, August.
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    Cited by:

    1. Garcés Díaz Daniel, 2017. "Explaining Inflation with a Classical Dichotomy Model and Switching Monetary Regimes: Mexico 1932-2013," Working Papers 2017-20, Banco de México.
    2. Nielsen, Heino Bohn, 2007. "A "maximum-eigenvalue" test for the cointegration ranks in I(2) vector autoregressions," Economics Letters, Elsevier, vol. 94(3), pages 445-451, March.
    3. M. Ege Yazgan & Ilknur Zer-Toker, 2010. "Currency substitution, policy rule and pass-through: evidence from Turkey," Applied Economics, Taylor & Francis Journals, vol. 42(18), pages 2365-2378.

    More about this item


    vector autoregression; error correction model; cointegration; I(2); likelihood ratio test; Monte Carlo; reduced rank; rank testing;

    JEL classification:

    • 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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