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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. Bent Nielsen & Eric Engler, 2007. "The empirical process of autoregressive residuals," Economics Papers 2007-W01, Economics Group, Nuffield College, University of Oxford.
  2. 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.
  3. 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.
  4. Bent Nielsen, 2001. "Order determination in general vector autoregressions," Economics Series Working Papers 2001-W10, University of Oxford, Department of Economics.
  5. Nielsen, Bent, 2010. "Analysis Of Coexplosive Processes," Econometric Theory, Cambridge University Press, vol. 26(03), pages 882-915, June.
  6. 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.
  7. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  8. 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.
  9. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, March.
  10. Johansen, S. & Schaumburg, E., 1997. "Likelihood Analysis of Seasonal Cointegration," Economics Working Papers eco97/16, European University Institute.
  11. Johansen, S., 1991. "A Statistical Analsysis of Cointegration for I(2) Variables," Papers 77, Helsinki - Department of Economics.
  12. 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.
  13. 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.
  14. Bent Nielsen, . "On the distribution of tests of cointegration rank," Economics Papers 1997-W10, Economics Group, Nuffield College, University of Oxford.
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