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Cointegration in Fractional Systems with Deterministic Trends

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  • Fabrizio Iacone
  • Peter M Robinson

Abstract

We consider a cointegrated system generated by processes that may be fractionally integrated, and by additive polynomial and generalized polynomial trends. In view of the consequent competition between stochastic and deterministic trends, we consider various estimates of the cointegrating vector and develop relevant asymptotic theory, including the situation where fractional orders of integration are unknown.

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File URL: http://sticerd.lse.ac.uk/dps/em/em476.pdf
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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2004/476.

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Date of creation: May 2004
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Handle: RePEc:cep:stiecm:/2004/476

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

Keywords: Fractional cointegration; deterministic trends; ordinary least squares estimation; generalized least squares estimation; Wald tests.;

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References

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  1. Peter M Robinson, 2004. "Efficiency Improvements in Inference on Stationary and Nonstationary Fractional Time Series," STICERD - Econometrics Paper Series /2004/480, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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  6. Perron, Pierre & Campbell, John Y, 1993. "A Note on Johansen's Cointegration Procedure When Trends Are Present," Empirical Economics, Springer, vol. 18(4), pages 777-89.
  7. Javier Hualde & Peter M Robinson, 2003. "Cointegration in Fractional Systems with Unkown Integration Orders," STICERD - Econometrics Paper Series /2003/449, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  8. Ogaki, M. & Park, Y.Y., 1989. "A Cointegration Approach To Estimating Preference Parameters," RCER Working Papers 209, University of Rochester - Center for Economic Research (RCER).
  9. D Marinucci & Peter M Robinson, 2001. "Semiparametric Fractional Cointegration Analysis," STICERD - Econometrics Paper Series /2001/420, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  10. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
  11. P.M. Robinson & D. Marinucci, 2000. "The Averaged Periodogram for Nonstationary Vector Time Series," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 149-160, January.
  12. Hassler, U. & Marmol, Francesc & Velasco, Carlos, . "Residual log-periodogram inference for long-run relationships," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4359, Universidad Carlos III de Madrid.
  13. Corbae, Dean & Ouliaris, Sam, 1988. "Cointegration and Tests of Purchasing Power Parity," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 508-11, August.
  14. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 99-125, January.
  15. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
  16. 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.
  17. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-12, January.
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  19. Velasco, Carlos, . "Gaussian semi-parametric estimation of fractional cointegration," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4356, Universidad Carlos III de Madrid.
  20. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
  21. 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, vol. 53(1-3), pages 211-244.
  22. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(04), pages 583-621, August.
  23. D Marinucci & Peter M Robinson, 2001. "Narrow-Band Analysis of Nonstationary Processes," STICERD - Econometrics Paper Series /2001/421, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  24. Velasco, Carlos & Robinson, Peter M., . "Whittle pseudo-maximum likelihood estimation for nonstationary time series," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4434, Universidad Carlos III de Madrid.
  25. Julia Campos & Neil R. Ericsson & David F. Hendry, 1993. "Cointegration tests in the presence of structural breaks," International Finance Discussion Papers 440, Board of Governors of the Federal Reserve System (U.S.).
  26. Robinson, P. M., 1986. "On the errors-in-variables problem for time series," Journal of Multivariate Analysis, Elsevier, vol. 19(2), pages 240-250, August.
  27. Juan J. Dolado & Francisco Mármol, 1996. "Efficient Estimation of Cointegrating Relationships Among Higher Order and Fractionally Integrated Processes," Banco de España Working Papers 9617, Banco de España.
  28. Hoffman, Dennis L & Rasche, Robert H, 1991. "Long-Run Income and Interest Elasticities of Money Demand in the United States," The Review of Economics and Statistics, MIT Press, vol. 73(4), pages 665-74, November.
  29. Marinucci, D. & Robinson, Peter M., 2001. "Narrow-band analysis of nonstationary processes," Open Access publications from London School of Economics and Political Science http://eprints.lse.ac.uk/, London School of Economics and Political Science.
  30. Hansen, Bruce E., 1992. "Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 87-121.
  31. D Marinucci & Peter M Robinson, 2000. "The Averaged Periodogram for Nonstationary Vector Time Series," STICERD - Econometrics Paper Series /2000/408, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  32. 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.
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Citations

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Cited by:
  1. Luis A. Gil-Alana, 2009. "Warming break trends and fractional integration in the northern, southern and global temperature anomaly series," Faculty Working Papers 09/09, School of Economics and Business Administration, University of Navarra.
  2. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, School of Economics and Management, University of Aarhus.
  3. Marzio Galeotti & Matteo Manera & Alessandro Lanza, 2006. "On the Robustness of Robustness Checks of the Environmental Kuznets Curve," Working Papers 20060501, Università degli Studi di Milano-Bicocca, Dipartimento di Statistica, revised May 2006.
  4. Luis Gil-Alana & Rolando Peláez, 2008. "The persistence of earnings per share," Review of Quantitative Finance and Accounting, Springer, vol. 31(4), pages 425-439, November.
  5. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
  6. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2007. "Long Run and Cyclical Dynamics in the US Stock Market," CESifo Working Paper Series 2046, CESifo Group Munich.
  7. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
  8. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2006. "Purchasing Power Parity: The Irish Experience Re-visited," Trinity Economics Papers tep200615, Trinity College Dublin, Department of Economics.

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