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Likelihood based testing for no fractional cointegration

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  • Katarzyna Lasak

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

Abstract

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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Bibliographic Info

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
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Handle: RePEc:aah:create:2008-52

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Error correction model; Gaussian VAR model; Maximum likelihood estimation; Fractional cointegration; Likelihood ratio tests; fractional Brownian motion;

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  1. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1367, Cowles Foundation for Research in Economics, Yale University, revised Jul 2004.
  2. Breitung, Jörg & Hassler, Uwe, 2000. "Inference on the cointegration rank in fractionally integrated processes," SFB 373 Discussion Papers, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 2000,65, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  3. Nielsen, Morten Oe., . "Multivariate Lagrange Multiplier Tests for Fractional Integration," Economics Working Papers, School of Economics and Management, University of Aarhus 2002-18, School of Economics and Management, University of Aarhus.
  4. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, Econometric Society, vol. 59(6), pages 1551-80, November.
  5. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, Econometric Society, vol. 58(1), pages 165-93, January.
  6. Willa Chen & Clifford Hurvich, 2004. "Semiparametric Estimation of Fractional Cointegrating Subspaces," Econometrics, EconWPA 0412007, EconWPA.
  7. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers, University of Rochester - Center for Economic Research (RCER) 296, University of Rochester - Center for Economic Research (RCER).
  8. 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, Cambridge University Press, vol. 22(06), pages 989-1029, December.
  9. Peter M Robinson & Yoshihiro Yajima, 2001. "Determination of Cointegrating Rank in Fractional Systems," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2001/423, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  10. Francesc Marmol & Carlos Velasco, 2004. "Consistent Testing of Cointegrating Relationships," Econometrica, Econometric Society, Econometric Society, vol. 72(6), pages 1809-1844, November.
  11. Ingolf Dittmann, 2004. "Error Correction Models for Fractionally Cointegrated Time Series," Journal of Time Series Analysis, Wiley Blackwell, Wiley Blackwell, vol. 25(1), pages 27-32, 01.
  12. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, Elsevier, vol. 105(1), pages 225-247, November.
  13. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, Elsevier, vol. 16(1), pages 121-130, May.
  14. Peter M. Robinson & Carlos Velasco, 2000. "Whittle pseudo-maximum likelihood estimation for nonstationary time series," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 2273, London School of Economics and Political Science, LSE Library.
  15. D Marinucci & Peter M. Robinson, 1998. "Semiparametric frequency domain analysis of fractional cointegration," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 2258, London School of Economics and Political Science, LSE Library.
  16. Peter M. Robinson & Javier Hualde, 2002. "Cointegration in Fractional Systems with Unknown Integration Orders," Faculty Working Papers, School of Economics and Business Administration, University of Navarra 07/02, School of Economics and Business Administration, University of Navarra.
  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, Wiley Blackwell, vol. 25(5), pages 691-700, 09.
  18. Javier Hualde & Carlos Velasco, . "Distribution-free Tests of Fractional Cointegration," Faculty Working Papers, School of Economics and Business Administration, University of Navarra 08/06, School of Economics and Business Administration, University of Navarra.
  19. 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, Department of Economics, University of Oxford, vol. 65(4), pages 517-529, 09.
  20. D Marinucci & Peter M. Robinson, 2001. "Semiparametric fractional cointegration analysis," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 2269, London School of Economics and Political Science, LSE Library.
  21. Gonzalo, J. & Lee, T.H., 1995. "Pitfalls in Testing for Long Run Relationships," Papers, Boston University - Department of Economics 38, Boston University - Department of Economics.
  22. Davidson, James, 2002. "A model of fractional cointegration, and tests for cointegration using the bootstrap," Journal of Econometrics, Elsevier, Elsevier, vol. 110(2), pages 187-212, October.
  23. Davidson, James, 2006. "Alternative bootstrap procedures for testing cointegration in fractionally integrated processes," Journal of Econometrics, Elsevier, Elsevier, vol. 133(2), pages 741-777, August.
  24. James G. MacKinnon & Alfred A. Haug & Leo Michelis, 1996. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," Working Papers, York University, Department of Economics 1996_07, York University, Department of Economics.
  25. 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, Department of Economics, University of Oxford, vol. 48(3), pages 213-28, August.
  26. Hassler, Uwe & Breitung, J rg, 2006. "A Residual-Based Lm-Type Test Against Fractional Cointegration," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 22(06), pages 1091-1111, December.
  27. Andersson, Michael K. & Gredenhoff, Mikael P., 1999. "On the maximum likelihood cointegration procedure under a fractional equilibrium error," Economics Letters, Elsevier, Elsevier, vol. 65(2), pages 143-147, November.
  28. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers, School of Economics and Management, University of Aarhus 2008-53, School of Economics and Management, University of Aarhus.
  29. Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 24(03), pages 651-676, June.
  30. Ignacio N. Lobato & Carlos Velasco, 2006. "Optimal Fractional Dickey-Fuller tests," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 9(3), pages 492-510, November.
  31. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 12(2-3), pages 231-254.
  32. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 251-76, March.
  33. Frank S. Nielsen, 2008. "Local polynomial Whittle estimation covering non-stationary fractional processes," CREATES Research Papers, School of Economics and Management, University of Aarhus 2008-28, School of Economics and Management, University of Aarhus.
  34. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 86(1), pages 103-120, March.
  35. Delgado, Miguel A. & Velasco, Carlos, 2005. "Sign tests for long-memory time series," Journal of Econometrics, Elsevier, Elsevier, vol. 128(2), pages 215-251, October.
  36. Carlos Velasco, 2003. "Gaussian Semi-parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, Wiley Blackwell, vol. 24(3), pages 345-378, 05.
  37. Lyhagen, Johan, 1998. "Maximum likelihood estimation of the multivariate fractional cointegrating model," Working Paper Series in Economics and Finance, Stockholm School of Economics 233, Stockholm School of Economics.
  38. 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, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2000/391, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  39. 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.
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Citations

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Cited by:
  1. Niels Haldrup & Robinson Kruse, 2014. "Discriminating between fractional integration and spurious long memory," CREATES Research Papers, School of Economics and Management, University of Aarhus 2014-19, School of Economics and Management, University of Aarhus.
  2. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers, School of Economics and Management, University of Aarhus 2008-53, School of Economics and Management, University of Aarhus.
  3. Katarzyna Lasak & Carlos Velasco, 2014. "Fractional Cointegration Rank Estimation," Tinbergen Institute Discussion Papers, Tinbergen Institute 14-021/III, Tinbergen Institute.
  4. Søren Johansen, 2010. "An Extension of Cointegration to Fractional Autoregressive Processes," Discussion Papers, University of Copenhagen. Department of Economics 10-28, University of Copenhagen. Department of Economics.
  5. Federico Carlini & Katarzyna Lasak, 2014. "On an Estimation Method for an Alternative Fractionally Cointegrated Model," Tinbergen Institute Discussion Papers, Tinbergen Institute 14-052/III, Tinbergen Institute.
  6. Federico Carlini & Katarzyna Lasak, 2014. "On an Estimation Method for an Alternative Fractionally Cointegrated Model," CREATES Research Papers, School of Economics and Management, University of Aarhus 2014-15, School of Economics and Management, University of Aarhus.

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