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Exact Local Whittle Estimation of Fractionally Cointegrated Systems

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  • Shimotsu, Katsumi

Abstract

Semiparametric estimation of a bivariate fractionally cointegrated system is considered. We propose a two-step procedure that accommodates both (asymptotically) stationary (d =1/2) stochastic trend and/or equilibrium error. A tapered version of the local Whittle estimator of Robinson (2008) is used as the first-stage estimator, and the second-stage estimator employs the exact local Whittle approach of Shimotsu and Phillips (2005). The consistency and asymptotic distribution of the two-step estimator are derived. The estimator of the memory parameters has the same Gaussian asymptotic distribution in both the stationary and nonstationary case. The convergence rate and the asymptotic distribution of the estimator of the cointegrating vector are affected by the difference between the memory parameters. Further, the estimator has a Gaussian asymptotic distribution when the difference between the memory parameters is less than 1/2.

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Bibliographic Info

Paper provided by Graduate School of Economics, Hitotsubashi University in its series Discussion Papers with number 2010-11.

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Length: 34 p.
Date of creation: Sep 2010
Date of revision:
Handle: RePEc:hit:econdp:2010-11

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Keywords: discrete Fourier transform; fractional cointegration; long memory; nonstationarity; semiparametric estimation; Whittle likelihood;

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References

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  1. Peter M Robinson, 2004. "The Distance between Rival Nonstationary Fractional Processes," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2004/468, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  2. 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.
  3. 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.
  4. Lobato, Ignacio N., 1999. "A semiparametric two-step estimator in a multivariate long memory model," Journal of Econometrics, Elsevier, Elsevier, vol. 90(1), pages 129-153, May.
  5. 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.
  6. Hassler, U. & Marmol, F. & Velasco, C., 2006. "Residual log-periodogram inference for long-run relationships," Journal of Econometrics, Elsevier, Elsevier, vol. 130(1), pages 165-207, January.
  7. Federico Bandi & Benoit Perron, 2003. "Long memory and the relation between implied and realized volatility," Econometrics, EconWPA 0305004, EconWPA.
  8. 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.
  9. Katsumi Shimotsu, 2003. "Gaussian semiparametric estimation of multivariate fractionally integrated processes," Economics Discussion Papers, University of Essex, Department of Economics 571, University of Essex, Department of Economics.
  10. Brunetti, Celso & Gilbert, Christopher L., 2000. "Bivariate FIGARCH and fractional cointegration," Journal of Empirical Finance, Elsevier, Elsevier, vol. 7(5), pages 509-530, December.
  11. Shimotsu, Katsumi & Phillips, Peter C.B., 2006. "Local Whittle estimation of fractional integration and some of its variants," Journal of Econometrics, Elsevier, Elsevier, vol. 130(2), pages 209-233, February.
  12. Katsumi Shimotsu & Morten Ørregaard Nielsen, 2006. "Determining the Cointegrating Rank in Nonstationary Fractional Systems by the Exact Local Whittle Approach," Working Papers, Queen's University, Department of Economics 1029, Queen's University, Department of Economics.
  13. D. Marinucci & Peter M. Robinson, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 303, London School of Economics and Political Science, LSE Library.
  14. Morten Ørregaard Nielsen & Per Frederiksen, 2011. "Fully modified narrow‐band least squares estimation of weak fractional cointegration," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 14(1), pages 77-120, February.
  15. Katsumi Shimotsu, 2006. "Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend," Working Papers, Queen's University, Department of Economics 1061, Queen's University, Department of Economics.
  16. Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Local Whittle Estimation in Nonstationary and Unit Root Cases," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1266, Cowles Foundation for Research in Economics, Yale University, revised Sep 2003.
  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. Davidson James E. H. & Peel David A & Byers J. David, 2006. "Support for Governments and Leaders: Fractional Cointegration Analysis of Poll Evidence from the UK, 1960-2004," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 10(1), pages 1-23, March.
  19. Shao, Xiaofeng & Wu, Wei Biao, 2007. "Local Whittle Estimation Of Fractional Integration For Nonlinear Processes," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 23(05), pages 899-929, October.
  20. Morten Oerregaard Nielsen, . "Local Whittle Analysis of Stationary Fractional Cointegration," Economics Working Papers, School of Economics and Management, University of Aarhus 2002-8, School of Economics and Management, University of Aarhus.
  21. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, Elsevier, vol. 105(1), pages 225-247, November.
  22. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, Elsevier, vol. 106(2), pages 217-241, February.
  23. 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.
  24. D Marinucci & Peter Robinson, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 2015, London School of Economics and Political Science, LSE Library.
  25. Tsay, Wen-Jen & Chung, Ching-Fan, 2000. "The spurious regression of fractionally integrated processes," Journal of Econometrics, Elsevier, Elsevier, vol. 96(1), pages 155-182, May.
  26. 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.
  27. 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.
  28. Cassola, Nuno & Morana, Claudio, 2010. "Comovements in volatility in the euro money market," Journal of International Money and Finance, Elsevier, Elsevier, vol. 29(3), pages 525-539, April.
  29. 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.
  30. Lobato, Ignacio N & Velasco, Carlos, 2000. "Long Memory in Stock-Market Trading Volume," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 18(4), pages 410-27, October.
  31. 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.
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Cited by:
  1. Gilles De Truchis & Benjamin Keddad, 2012. "South East Asian Monetary Integration: New Evidences from Fractional Cointegration of Real Exchange Rates," Working Papers, HAL halshs-00793503, HAL.
  2. Marcel Aloy & Gilles de Truchis, 2013. "Optimal Estimation Strategies for Bivariate Fractional Cointegration Systems," AMSE Working Papers 1353, Aix-Marseille School of Economics, Marseille, France, revised 29 Oct 2013.

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