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Testing of Fractional Cointegration in Macroeconomic Time Series

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  • Luis A. Gil-Alana

Abstract

We propose in this article a two-step testing procedure of fractional cointegration in macroeconomic time series. It is based on Robinson's ("Journal of the American Statistical Association", Vol. 89, p. 1420) univariate tests and is similar in spirit to the one proposed by Engle & Granger ("Econometrica", Vol. 55, p. 251), testing initially the order of integration of the individual series and then, testing the degree of integration of the residuals from the cointegrating relationship. Finite-sample critical values of the new tests are computed and Monte Carlo experiments are conducted to examine the size and the power properties of the tests in finite samples. An empirical application, using the same datasets as in Engle & Granger ("Econometrica", Vol. 55, p. 251) and Campbell & Shiller ("Journal of Political Economy", Vol. 95, p. 1062), is also carried out at the end of the article. Copyright 2003 Blackwell Publishing Ltd.

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Bibliographic Info

Article provided by Department of Economics, University of Oxford in its journal Oxford Bulletin of Economics and Statistics.

Volume (Year): 65 (2003)
Issue (Month): 4 (09)
Pages: 517-529

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Handle: RePEc:bla:obuest:v:65:y:2003:i:4:p:517-529

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  1. John Y. Campbell & Robert J. Shiller, 1986. "Cointegration and Tests of Present Value Models," Cowles Foundation Discussion Papers 785, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  4. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
  5. D Marinucci & Peter M. Robinson, 1998. "Semiparametric frequency domain analysis of fractional cointegration," LSE Research Online Documents on Economics 2258, London School of Economics and Political Science, LSE Library.
  6. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  8. Javier Hualde & Peter M Robinson, 2006. "Root-N-Consistent Estimation Of Weakfractional Cointegration," STICERD - Econometrics Paper Series /2006/499, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  9. 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.
  10. 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.
  11. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  12. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
  13. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, September.
  14. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  15. Juan J. Dolado & Francisco Mármol, 1996. "Efficient Estimation of Cointegrating Relationships Among Higher Order and Fractionally Integrated Processes," Banco de Espa�a Working Papers 9617, Banco de Espa�a.
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Citations

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Cited by:
  1. 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.
  2. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2005. "Testing for Long Memory and Nonlinear Time Series: A Demand for Money Study," Trinity Economics Papers tep20021, Trinity College Dublin, Department of Economics.
  3. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2014. "Youth Unemployment in Europe: Persistence and Macroeconomic Determinants," CESifo Working Paper Series 4696, CESifo Group Munich.
  4. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
  5. Burcu Kiran, 2011. "Fractional Cointegration Relationship between Oil Prices and Stock Markets: An Empirical Analysis from G7 Countries," Prague Economic Papers, University of Economics, Prague, vol. 2011(2), pages 177-189.
  6. Luis Gil-Alana, 2004. "Forecasting the real output using fractionally integrated techniques," Applied Economics, Taylor & Francis Journals, vol. 36(14), pages 1583-1589.
  7. Luis Alberiko Gil-Alana, 2002. "Multivariate Tests of Fractionally Integrated Hypotheses," Faculty Working Papers 09/02, School of Economics and Business Administration, University of Navarra.
  8. Katarzyna Lasak & Carlos Velasco, 2013. "Fractional cointegration rank estimation," CREATES Research Papers 2013-08, School of Economics and Management, University of Aarhus.
  9. repec:ise:isegwp:wp182008 is not listed on IDEAS
  10. Burcu Kiran, 2013. "A fractional cointegration analysis of Fisher hypothesis: evidence from Turkey," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(2), pages 1077-1084, February.
  11. Cunado, J. & Gil-Alana, L.A. & de Gracia, F. Perez, 2005. "A test for rational bubbles in the NASDAQ stock index: A fractionally integrated approach," Journal of Banking & Finance, Elsevier, vol. 29(10), pages 2633-2654, October.
  12. J. Cunado & L.A. Gil-Alana & F. Pérez de Gracia,, 2007. "Real convergence in some emerging countries: a fractionally integrated approach," Recherches économiques de Louvain, De Boeck Université, vol. 73(3), pages 293-310.
  13. Gil-Alana, L.A., 2008. "Testing of seasonal integration and cointegration with fractionally integrated techniques: An application to the Danish labour demand," Economic Modelling, Elsevier, vol. 25(2), pages 326-339, March.
  14. Daiki Maki, 2013. "Detecting cointegration relationships under nonlinear models: Monte Carlo analysis and some applications," Empirical Economics, Springer, vol. 45(1), pages 605-625, August.
  15. Evans, Mark, 2011. "Steel consumption and economic activity in the UK: The integration and cointegration debate," Resources Policy, Elsevier, vol. 36(2), pages 97-106, June.
  16. Cunado, J. & Gil-Alana, L. A. & Perez de Gracia, F., 2004. "Is the US fiscal deficit sustainable?: A fractionally integrated approach," Journal of Economics and Business, Elsevier, vol. 56(6), pages 501-526.
  17. Gianluca Moretti, 2007. "Detecting long memory co-movements in macroeconomic time series," Temi di discussione (Economic working papers) 642, Bank of Italy, Economic Research and International Relations Area.
  18. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2007. "Demand for Money: A Study in Testing Time Series for Long Memory and Nonlinearity," The Economic and Social Review, Economic and Social Studies, vol. 38(1), pages 1-24.

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