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Likelihood based testing for no fractional cointegration

  • Katarzyna Lasak

    ()

    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

We consider two likelihood ratio tests, so-called maximum eigenvalue and trace tests, for the null of no cointegration when fractional cointegration is allowed under the alternative, which is a first step to generalize the so-called Johansen's procedure to the fractional cointegration case. The standard cointegration analysis only considers the assumption that deviations from equilibrium can be integrated of order zero, which is very restrictive in many cases and may imply an important loss of power in the fractional case. We consider the alternative hypotheses with equilibrium deviations that can be mean reverting with order of integration possibly greater than zero. Moreover, the degree of fractional cointegration is not assumed to be known, and the asymptotic null distribution of both tests is found when considering an interval of possible values. The power of the proposed tests under fractional alternatives and size accuracy provided by the asymptotic distribution in finite samples are investigated.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-52.

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Length: 25
Date of creation: 11 Sep 2008
Date of revision:
Handle: RePEc:aah:create:2008-52
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Joerg Breitung and Uwe Hassler, 2001. "Inference on the Cointegration Rank in Fractionally Integrated Processes," Computing in Economics and Finance 2001 233, Society for Computational Economics.
  2. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, School of Economics and Management, University of Aarhus.
  3. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
  4. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  5. Michael Dueker & Richard Startz, 1998. "Maximum-Likelihood Estimation Of Fractional Cointegration With An Application To U.S. And Canadian Bond Rates," The Review of Economics and Statistics, MIT Press, vol. 80(3), pages 420-426, August.
  6. Willa Chen & Clifford Hurvich, 2004. "Semiparametric Estimation of Fractional Cointegrating Subspaces," Econometrics 0412007, EconWPA.
  7. Giraitis, Liudas & Leipus, Remigijus & Philippe, Anne, 2006. "A Test For Stationarity Versus Trends And Unit Roots For A Wide Class Of Dependent Errors," Econometric Theory, Cambridge University Press, vol. 22(06), pages 989-1029, December.
  8. Nielsen, Morten Oe., . "Multivariate Lagrange Multiplier Tests for Fractional Integration," Economics Working Papers 2002-18, School of Economics and Management, University of Aarhus.
  9. Carlos Velasco, 2003. "Gaussian Semi-parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, 05.
  10. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
  11. Gonzalo, Jesus & Lee, Tae-Hwy, 1998. "Pitfalls in testing for long run relationships," Journal of Econometrics, Elsevier, vol. 86(1), pages 129-154, June.
  12. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  13. Delgado, Miguel A. & Velasco, Carlos, 2005. "Sign tests for long-memory time series," Journal of Econometrics, Elsevier, vol. 128(2), pages 215-251, October.
  14. Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, vol. 24(03), pages 651-676, June.
  15. Ignacio N. Lobato & Carlos Velasco, 2006. "Optimal Fractional Dickey-Fuller tests," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 492-510, November.
  16. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Economics Discussion Papers 535, University of Essex, Department of Economics.
  17. Luis A. Gil-Alana, 2004. "A joint test of fractional integration and structural breaks at a known period of time," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 691-700, 09.
  18. James G. MacKinnon & Alfred A. Haug & Leo Michelis, 1996. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," Working Papers 1996_07, York University, Department of Economics.
  19. Andersson, Michael K. & Gredenhoff, Mikael P., 1999. "On the maximum likelihood cointegration procedure under a fractional equilibrium error," Economics Letters, Elsevier, vol. 65(2), pages 143-147, November.
  20. D Marinucci & Peter M. Robinson, 2001. "Semiparametric fractional cointegration analysis," LSE Research Online Documents on Economics 2269, London School of Economics and Political Science, LSE Library.
  21. Javier Hualde & Carlos Velasco, . "Distribution-free Tests of Fractional Cointegration," Faculty Working Papers 08/06, School of Economics and Business Administration, University of Navarra.
  22. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  23. P. M. Robinson & J. Hualde, 2003. "Cointegration in Fractional Systems with Unknown Integration Orders," Econometrica, Econometric Society, vol. 71(6), pages 1727-1766, November.
  24. Dittmann, Ingolf, 2000. "Error correction models for fractionally cointegrated time series," Technical Reports 2000,02, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  25. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  26. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
  27. D Marinucci & Peter M. Robinson, 1998. "Semiparametric frequency domain analysis of fractional cointegration," LSE Research Online Documents on Economics 2258, London School of Economics and Political Science, LSE Library.
  28. Luis A. Gil-Alana, 2003. "Testing of Fractional Cointegration in Macroeconomic Time Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(4), pages 517-529, 09.
  29. D Marinucci & Peter M Robinson, 2001. "Semiparametric Fractional Cointegration Analysis," STICERD - Econometrics Paper Series /2001/420, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  30. Peter M. Robinson & Carlos Velasco, 2000. "Whittle pseudo-maximum likelihood estimation for nonstationary time series," LSE Research Online Documents on Economics 2273, London School of Economics and Political Science, LSE Library.
  31. Peter M Robinson & Carlos Velasco, 2000. "Whittle Pseudo-Maximum Likelihood Estimation for Nonstationary Time Series - (Now published in Journal of the American Statistical Association, 95, (2000), pp.1229-1243.)," STICERD - Econometrics Paper Series /2000/391, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  32. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
  33. Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-28, August.
  34. Francesc Marmol & Carlos Velasco, 2004. "Consistent Testing of Cointegrating Relationships," Econometrica, Econometric Society, vol. 72(6), pages 1809-1844, November.
  35. Frank S. Nielsen, 2008. "Local polynomial Whittle estimation covering non-stationary fractional processes," CREATES Research Papers 2008-28, School of Economics and Management, University of Aarhus.
  36. Lyhagen, Johan, 1998. "Maximum likelihood estimation of the multivariate fractional cointegrating model," SSE/EFI Working Paper Series in Economics and Finance 233, Stockholm School of Economics.
  37. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  38. Davidson, James, 2002. "A model of fractional cointegration, and tests for cointegration using the bootstrap," Journal of Econometrics, Elsevier, vol. 110(2), pages 187-212, October.
  39. Hassler, Uwe & Breitung, J rg, 2006. "A Residual-Based Lm-Type Test Against Fractional Cointegration," Econometric Theory, Cambridge University Press, vol. 22(06), pages 1091-1111, December.
  40. Davidson, James, 2006. "Alternative bootstrap procedures for testing cointegration in fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 741-777, August.
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