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Maximum likelihood estimation of fractionally cointegrated systems

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  • Katarzyna Lasak

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

Abstract

In this paper we consider a fractionally cointegrated error correction model and investigate asymptotic properties of the maximum likelihood (ML) estimators of the matrix of the cointe- gration relations, the degree of fractional cointegration, the matrix of the speed of adjustment to the equilibrium parameters and the variance-covariance matrix of the error term. We show that using ML principles to estimate jointly all parameters of the fractionally cointegrated system we obtain consistent estimates and provide their asymptotic distributions. The cointegration matrix is asymptotically mixed normal distributed, while the degree of fracional cointegration and the speed of adjustment to the equilibrium matrix have joint normal distribution, which proves the intuition that the memory of the cointegrating residuals affects the speed of conver- gence to the long-run equilibrium, but does not have any influence on the long-run relationship. The rate of convergence of the estimators of the long-run relationships depends on the coin- tegration degree but it is optimal for the strong cointegration case considered. We also prove that misspecification of the degree of fractional cointegation does not affect the consistency of the estimators of the cointegration relationships, although usual inference rules are not valid. We illustrate our results in finite samples by Monte Carlo analysis.

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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 2008-53.

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Length: 37
Date of creation: 12 Sep 2008
Date of revision:
Handle: RePEc:aah:create:2008-53

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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;

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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, Society for Computational Economics 233, Society for Computational Economics.
  2. 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.
  3. Francesc Marmol & Carlos Velasco, 2004. "Consistent Testing of Cointegrating Relationships," Econometrica, Econometric Society, Econometric Society, vol. 72(6), pages 1809-1844, November.
  4. 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.
  5. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, Elsevier, vol. 105(1), pages 225-247, November.
  6. Juan J. Dolado & Francesc Marmol, 2004. "Asymptotic inference results for multivariate long-memory processes," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 7(1), pages 168-190, 06.
  7. Javier Hualde & Peter Robinson, . "Semiparametric Estimation of Fractional Cointegration," Faculty Working Papers, School of Economics and Business Administration, University of Navarra 07/06, School of Economics and Business Administration, University of Navarra.
  8. 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.
  9. Willa Chen & Clifford Hurvich, 2004. "Semiparametric Estimation of Fractional Cointegrating Subspaces," Econometrics, EconWPA 0412007, EconWPA.
  10. Donald W.K. Andrews & Yixiao Sun, 2002. "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1384, Cowles Foundation for Research in Economics, Yale University.
  11. Morten Ørregaard Nielsen & Per Frederiksen, 2008. "Fully Modified Narrow-Band Least Squares Estimation of Stationary Fractional Cointegration," Working Papers, Queen's University, Department of Economics 1171, Queen's University, Department of Economics.
  12. 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.
  13. 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.
  14. Robinson, P.M. & Iacone, F., 2005. "Cointegration in fractional systems with deterministic trends," Journal of Econometrics, Elsevier, Elsevier, vol. 129(1-2), pages 263-298.
  15. 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.
  16. Javier Hualde & A Robinson, 2006. "Root-N-Consistent Estimation Of Weakfractional Cointegration," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /06/499, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  17. 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.
  18. 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.
  19. 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.
  20. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 12(2-3), pages 231-254.
  21. Christensen, Bent Jesper & Nielsen, Morten Orregaard, 2006. "Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting," Journal of Econometrics, Elsevier, Elsevier, vol. 133(1), pages 343-371, July.
  22. 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.
  23. 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.
  24. Chen, Willa W. & Hurvich, Clifford M., 2003. "Semiparametric Estimation of Multivariate Fractional Cointegration," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 98, pages 629-642, January.
  25. Uwe Hassler & Francesc Marmol & C. Velasco, 2000. "Fractional Cointegrating Regression In The Presence Of Linear Time Trends," Computing in Economics and Finance 2000, Society for Computational Economics 138, Society for Computational Economics.
  26. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, Elsevier, vol. 158(1), pages 67-77, September.
  27. Nielsen, Morten Orregaard, 2007. "Local Whittle Analysis of Stationary Fractional Cointegration and the ImpliedRealized Volatility Relation," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 25, pages 427-446, October.
  28. 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.
  29. 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.
  30. 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.
  31. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, Econometric Society, vol. 58(1), pages 113-44, January.
  32. 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.
  33. Peter C.B. Phillips & Bruce E. Hansen, 1988. "Statistical Inference in Instrumental Variables," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 869R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1989.
  34. Chen, Willa W. & Hurvich, Clifford M., 2003. "Estimating fractional cointegration in the presence of polynomial trends," Journal of Econometrics, Elsevier, Elsevier, vol. 117(1), pages 95-121, November.
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Citations

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Cited by:
  1. Katarzyna Lasak, 2008. "Likelihood based testing for no fractional cointegration," CREATES Research Papers, School of Economics and Management, University of Aarhus 2008-52, School of Economics and Management, University of Aarhus.
  2. Eduardo Rossi & Paolo Santucci de Magistris, 2009. "A No Arbitrage Fractional Cointegration Analysis Of The Range Based Volatility," CREATES Research Papers, School of Economics and Management, University of Aarhus 2009-31, School of Economics and Management, University of Aarhus.
  3. Massimiliano Caporin & Angelo Ranaldo, 2011. "On the Predictability of Stock Prices: a Case for High and Low Prices," Working Papers 2011-11, Swiss National Bank.
  4. 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.
  5. 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.
  6. Marcel Aloy & Gilles de Truchis, 2012. "Estimation and Testing for Fractional Cointegration," AMSE Working Papers, Aix-Marseille School of Economics, Marseille, France 1215, Aix-Marseille School of Economics, Marseille, France.
  7. 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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