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Test for cointegration rank in general vector autoregressions

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  • B. Nielsen

    () (Dept of Economics and Nuffield College, University of Oxford, Oxford.)

Abstract

Johansen derived the asymptotic theory for his cointegration rank test statisic for a vector autoregression where the parameters are restricted so the process is integrated of order one. It is investigated to what extent these parameter restrictions are binding. The eigenvalues of Johansen’s eigenvalue problem are shown to have the same consistency rates accross the parameter space. The test statistic is shown to have the usual asymptotic distribution as long as the possibilities of additional unit roots and of singular explosiveness are ruled out. To prove the results the convergence of stochastic integrals with respect to singular explosive processes is considered.

Suggested Citation

  • B. Nielsen, 2009. "Test for cointegration rank in general vector autoregressions," Economics Papers 2009-W10, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:0910
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    File URL: http://www.nuffield.ox.ac.uk/economics/papers/2009/w10/VARunstable.pdf
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    References listed on IDEAS

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    1. Johansen, Soren & Schaumburg, Ernst, 1998. "Likelihood analysis of seasonal cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 301-339, November.
    2. Johansen, Søren, 1995. "A Stastistical Analysis of Cointegration for I(2) Variables," Econometric Theory, Cambridge University Press, vol. 11(01), pages 25-59, February.
    3. Nielsen, Bent, 2001. "The Asymptotic Distribution of Unit Root Tests of Unstable Autoregressive Processes," Econometrica, Econometric Society, vol. 69(1), pages 211-219, January.
    4. la Cour, Lisbeth, 1998. "A Parametric Characterization Of Integrated Vector Autoregressive (Var) Processes," Econometric Theory, Cambridge University Press, vol. 14(02), pages 187-199, April.
    5. E ric E ngler & B ent N ielsen, 2009. "The empirical process of autoregressive residuals," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 367-381, July.
    6. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    7. Bauer, Dietmar, 2009. "Almost Sure Bounds On The Estimation Error For Ols Estimators When The Regressors Include Certain Mfi(1) Processes," Econometric Theory, Cambridge University Press, vol. 25(02), pages 571-582, April.
    8. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(05), pages 621-642, October.
    9. Bent Nielsen, "undated". "On the distribution of tests of cointegration rank," Economics Papers 1997-W10, Economics Group, Nuffield College, University of Oxford.
    10. Nielsen, Bent, 2010. "Analysis Of Coexplosive Processes," Econometric Theory, Cambridge University Press, vol. 26(03), pages 882-915, June.
    11. Bent Nielsen, 2006. "Correlograms for non-stationary autoregressions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 707-720.
    12. Bent Nielsen, 2001. "Order determination in general vector autoregressions," Economics Papers 2001-W10, Economics Group, Nuffield College, University of Oxford.
    13. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    14. Phillips, Peter C.B. & Magdalinos, Tassos, 2008. "Limit Theory For Explosively Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 24(04), pages 865-887, August.
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    Cited by:

    1. Hallin, M. & van den Akker, R. & Werker, B.J.M., 2012. "Rank-based Tests of the Cointegrating Rank in Semiparametric Error Correction Models," Discussion Paper 2012-089, Tilburg University, Center for Economic Research.
    2. Hallin, M. & Werker, B.J.M. & van den Akker, R., 2015. "Optimal Pseudo-Gaussian and Rank-based Tests of the Cointegration Rank in Semiparametric Error-correction Models," Discussion Paper 2015-001, Tilburg University, Center for Economic Research.
    3. Hallin, Marc & van den Akker, Ramon & Werker, Bas J.M., 2016. "Semiparametric error-correction models for cointegration with trends: Pseudo-Gaussian and optimal rank-based tests of the cointegration rank," Journal of Econometrics, Elsevier, vol. 190(1), pages 46-61.

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