IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: ftp://ftp.econ.au.dk/creates/rp/08/rp08_52.pdf
Download Restriction: no

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

as
in new window

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/

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. 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.
  2. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Cowles Foundation Discussion Papers 1367, Cowles Foundation for Research in Economics, Yale University, revised Jul 2004.
  3. 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.
  4. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-93, January.
  5. D Marinucci & Peter M Robinson, 2001. "Semiparametric Fractional Cointegration Analysis," STICERD - Econometrics Paper Series 420, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  6. 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).
  7. Delgado, Miguel A. & Velasco, Carlos, 2005. "Sign tests for long-memory time series," Journal of Econometrics, Elsevier, vol. 128(2), pages 215-251, October.
  8. 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.
  9. 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.
  10. Ingolf Dittmann, 2004. "Error Correction Models for Fractionally Cointegrated Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 27-32, 01.
  11. 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.
  12. Breitung, Jörg & Hassler, Uwe, 2000. "Inference on the cointegration rank in fractionally integrated processes," SFB 373 Discussion Papers 2000,65, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  13. 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.
  14. 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.
  15. Morten �rregaard Nielsen, 2005. "Multivariate Lagrange Multiplier Tests for Fractional Integration," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(3), pages 372-398.
  16. Hualde, Javier & Velasco, Carlos, 2008. "Distribution-Free Tests Of Fractional Cointegration," Econometric Theory, Cambridge University Press, vol. 24(01), pages 216-255, February.
  17. 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.
  18. 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.
  19. P. M. Robinson & J. Hualde, 2003. "Cointegration in Fractional Systems with Unknown Integration Orders," Econometrica, Econometric Society, vol. 71(6), pages 1727-1766, November.
  20. 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.
  21. Ignacio N. Lobato & Carlos Velasco, 2006. "Optimal Fractional Dickey-Fuller tests," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 492-510, November.
  22. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  23. repec:cep:stiecm:/2001/420 is not listed on IDEAS
  24. 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.
  25. Francesc Marmol & Carlos Velasco, 2004. "Consistent Testing of Cointegrating Relationships," Econometrica, Econometric Society, vol. 72(6), pages 1809-1844, November.
  26. 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.
  27. Carlos Velasco, 2003. "Gaussian Semi-parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, 05.
  28. 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.
  29. 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.
  30. 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.
  31. Luis A. Gil-Alana, 2003. "Testing of Fractional Cointegration in Macroeconomic Time Series," Faculty Working Papers 09/03, School of Economics and Business Administration, University of Navarra.
  32. Davidson, James, 2006. "Alternative bootstrap procedures for testing cointegration in fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 741-777, August.
  33. 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.
  34. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
  35. Willa Chen & Clifford Hurvich, 2004. "Semiparametric Estimation of Fractional Cointegrating Subspaces," Econometrics 0412007, EconWPA.
  36. Gonzalo, J. & Lee, T.H., 1995. "Pitfalls in Testing for Long Run Relationships," Papers 38, Boston University - Department of Economics.
  37. 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.
  38. 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.
  39. repec:cep:stiecm:/2000/391 is not listed on IDEAS
  40. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
  41. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, School of Economics and Management, University of Aarhus.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:aah:create:2008-52. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.