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Test for cointegration rank in general vector autoregressions

  • B. Nielsen

    ()

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

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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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
Contact details of provider: Web page: http://www.nuff.ox.ac.uk/economics/

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  1. Johansen, Søren, 1995. "A Stastistical Analysis of Cointegration for I(2) Variables," Econometric Theory, Cambridge University Press, vol. 11(01), pages 25-59, February.
  2. Johansen, Soren & Schaumburg, Ernst, 1998. "Likelihood analysis of seasonal cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 301-339, November.
  3. Bent Nielsen & Eric Engler, 2007. "The empirical process of autoregressive residuals," Economics Papers 2007-W01, Economics Group, Nuffield College, University of Oxford.
  4. Nielsen, Bent, 2010. "Analysis Of Coexplosive Processes," Econometric Theory, Cambridge University Press, vol. 26(03), pages 882-915, June.
  5. 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.
  6. Bent Nielsen, 1999. "The Asymptotic Distribution of Unit Root Tests of Unstable Autoregressive Processes," Economics Series Working Papers 1999-W19, University of Oxford, Department of Economics.
  7. Bent Nielsen, 2001. "Order determination in general vector autoregressions," Economics Papers 2001-W10, Economics Group, Nuffield College, University of Oxford.
  8. Peter C.B. Phillips & Tassos Magdalinos, 2007. "Limit Theory for Explosively Cointegrated Systems," Cowles Foundation Discussion Papers 1614, Cowles Foundation for Research in Economics, Yale University.
  9. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  10. Bent Nielsen, 2003. "Correlograms for non-stationary autoregressions," Economics Papers 2003-W11, Economics Group, Nuffield College, University of Oxford.
  11. 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.
  12. Bent Nielsen, . "On the distribution of tests of cointegration rank," Economics Papers 1997-W10, Economics Group, Nuffield College, University of Oxford.
  13. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, March.
  14. 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.
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