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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.

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File URL: http://www.nuffield.ox.ac.uk/economics/papers/2009/w10/VARunstable.pdf
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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2009-W10.

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Length: 28 pages
Date of creation: 22 Sep 2009
Date of revision:
Handle: RePEc:nuf:econwp:0910

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Web page: http://www.nuff.ox.ac.uk/economics/

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References

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  1. 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, 07.
  2. Bent Nielsen, 2003. "Correlograms for non-stationary autoregressions," Economics Papers 2003-W11, Economics Group, Nuffield College, University of Oxford.
  3. Davidson, James & de Jong, Robert M., 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals Ii," Econometric Theory, Cambridge University Press, vol. 16(05), pages 643-666, October.
  4. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  5. 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.
  6. Johansen, Soren & Schaumburg, Ernst, 1998. "Likelihood analysis of seasonal cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 301-339, November.
  7. Bent Nielsen, 2001. "Order determination in general vector autoregressions," Economics Series Working Papers 2001-W10, University of Oxford, Department of Economics.
  8. 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.
  9. Bent Nielsen, . "On the distribution of tests of cointegration rank," Economics Papers 1997-W10, Economics Group, Nuffield College, University of Oxford.
  10. Bent Nielsen, 2005. "Analysis of co-explosive processes," Economics Papers 2005-W08, Economics Group, Nuffield College, University of Oxford.
  11. Nielsen, Bent, 2001. "The Asymptotic Distribution of Unit Root Tests of Unstable Autoregressive Processes," Econometrica, Econometric Society, vol. 69(1), pages 211-19, January.
  12. 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.
  13. Johansen, Søren, 1995. "A Stastistical Analysis of Cointegration for I(2) Variables," Econometric Theory, Cambridge University Press, vol. 11(01), pages 25-59, February.
  14. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
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Cited by:
  1. Marc Hallin & Ramon van den Akker & Bas Werker, 2012. "Rank-Based Tests of the Cointegrating Rank in Semiparametric Error Correction Models," Working Papers ECARES ECARES 2012-042, ULB -- Universite Libre de Bruxelles.

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