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Maximum likelihood estimation of the multivariate fractional cointegrating model

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  • Lyhagen, Johan

    ()
    (Dept. of Economic Statistics, Stockholm School of Economics)

Abstract

Departures from an economic equilibrium should be mean reverting. The deviations are often assumed to be integrated of order zero but this is too restrictive. It is sufficient that the shocks are integrated of an order less than one, i.e. they may be fractionally integrated. A fractionally cointegrated system is developed. Further, estimation and testing are discussed, analytically and by Monte Carlo simulations. The Monte Carlo simulations shows that it is much more severe to ignore fractional cointegration than incorporating it when it is not present.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 233.

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Length: 22 pages
Date of creation: 22 Apr 1998
Date of revision:
Handle: RePEc:hhs:hastef:0233

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Keywords: Fractional integration; Granger representation theorem; Likelihood ratio test; Monte Carlo.;

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References

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  1. Baillie, Richard T & Bollerslev, Tim, 1994. " Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, American Finance Association, vol. 49(2), pages 737-45, June.
  2. 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.
  3. 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.
  4. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198774501, October.
  5. Johansen, Søren & Juselius, Katarina, 1992. "Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK," Journal of Econometrics, Elsevier, Elsevier, vol. 53(1-3), pages 211-244.
  6. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 12(2-3), pages 231-254.
  7. Hylleberg, Svend & Mizon, Grayham E, 1989. "Cointegration and Error Correction Mechanisms," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 99(395), pages 113-25, Supplemen.
  8. Andersson, Michael K. & Gredenhoff, Mikael P., 1998. "Power and Bias of Likelihood Based Inference in the Cointegration Model under Fractional Cointegration," Working Paper Series in Economics and Finance, Stockholm School of Economics 221, Stockholm School of Economics.
  9. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, Econometric Society, vol. 58(2), pages 495-505, March.
  10. Banerjee, Anindya & Dolado, Juan J. & Galbraith, John W. & Hendry, David, 1993. "Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198288107, October.
  11. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 11(1), pages 103-12, January.
  12. 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.
  13. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, Elsevier, vol. 53(1-3), pages 165-188.
  14. Li, Hongyi & Maddala, G. S., 1997. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, Elsevier, vol. 80(2), pages 297-318, October.
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Cited by:
  1. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 20(3), pages 247-318.
  2. Katarzyna Lasak & Carlos Velasco, 2013. "Fractional cointegration rank estimation," CREATES Research Papers 2013-08, School of Economics and Management, University of Aarhus.
  3. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, School of Economics and Management, University of Aarhus.
  4. Katarzyna Lasak, 2008. "Likelihood based testing for no fractional cointegration," CREATES Research Papers 2008-52, School of Economics and Management, University of Aarhus.

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