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Long Memory and Fractional Integration in High Frequency Data on the US Dollar / British Pound Spot Exchange Rate

  • Guglielmo Maria Caporale
  • Luis A. Gil-Alana

This paper analyses the long-memory properties of a high-frequency financial time series dataset. It focuses on temporal aggregation and other features of the data, and how they might affect the degree of dependence of the series. Fractional integration or I(d) models are estimated with a variety of specifications for the error term. In brief, we find evidence that a lower degree of integration is associated with lower data frequencies. In particular, when the data are collected every 10 minutes there are several cases with values of d strictly smaller than 1, implying mean-reverting behaviour; however, for higher data frequencies the unit root null cannot be rejected. This holds for all four series examined, namely Open, High, Low and Last observations for the US dollar / British pound spot exchange rate and for different sample periods.

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File URL: http://www.diw.de/documents/publikationen/73/diw_01.c.420510.de/dp1294.pdf
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Paper provided by DIW Berlin, German Institute for Economic Research in its series Discussion Papers of DIW Berlin with number 1294.

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Length: 30 p.
Date of creation: 2013
Date of revision:
Handle: RePEc:diw:diwwpp:dp1294
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  1. Gil-Alana, Luis A., 2000. "Mean reversion in the real exchange rates," Economics Letters, Elsevier, vol. 69(3), pages 285-288, December.
  2. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
  3. I.N. Lobato & N.E. Savin, 1996. "Real and Spurious Long Memory Properties of Stock Market Data," Econometrics 9605004, EconWPA, revised 26 Sep 1996.
  4. G. Dufrenot & L. Mathieu & V. Mignon, & A. Peguin-Feissolle, 2002. "Persistent misalignments of the European exchange rates : some evidence from nonlinear cointegration," THEMA Working Papers 2002-29, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
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  6. Gilles Dufrénot & Sandrine Lardic & Laurent Mathieu & Valérie Mignon & Anne Peguin-Feissolle, 2008. "Explaining the European exchange rates deviations: long memory or nonlinear adjustment?," Post-Print halshs-00390141, HAL.
  7. Philipp Sibbertsen, 2004. "Long memory in volatilities of German stock returns," Empirical Economics, Springer, vol. 29(3), pages 477-488, 09.
  8. Leonardo Rocha Souza, 2008. "Why Aggregate Long Memory Time Series?," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 298-316.
  9. Souza, Leonardo Rocha, 2003. "A note on Chambers's "long memory and aggregation in macroeconomic time series"," Economics Working Papers (Ensaios Economicos da EPGE) 503, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  10. Souza, Leonardo R. & Smith, Jeremy, 2002. "Bias in the memory parameter for different sampling rates," International Journal of Forecasting, Elsevier, vol. 18(2), pages 299-313.
  11. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 280-83, July.
  12. 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.
  13. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
  14. John Cotter, 2011. "Uncovering Long Memory in High Frequency UK Futures," Papers 1103.5651, arXiv.org.
  15. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-313, September.
  16. Wang, Changyun, 2004. "Futures trading activity and predictable foreign exchange market movements," Journal of Banking & Finance, Elsevier, vol. 28(5), pages 1023-1041, May.
  17. Ohanissian, Arek & Russell, Jeffrey R. & Tsay, Ruey S., 2008. "True or Spurious Long Memory? A New Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 161-175, April.
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  20. Lobato, Ignacio N. & Velasco, Carlos, 2005. "Efficient wald tests for fractional unit roots," UC3M Working papers. Economics we056935, Universidad Carlos III de Madrid. Departamento de Economía.
  21. Caporale, Guglielmo Maria & Gil-Alana, Luis A., 2002. "Fractional integration and mean reversion in stock prices," The Quarterly Review of Economics and Finance, Elsevier, vol. 42(3), pages 599-609.
  22. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
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  24. Marcel Aloy & Mohamed Boutahar & Karine Gente & Anne Peguin-Feissolle, 2011. "Purchasing power parity and the long memory properties of real exchange rates: does one size fit all?," Working Papers halshs-00559170, HAL.
  25. Demetrescu, Matei & Kuzin, Vladimir & Hassler, Uwe, 2008. "Long Memory Testing In The Time Domain," Econometric Theory, Cambridge University Press, vol. 24(01), pages 176-215, February.
  26. Christopher F. Baum & John Barkoulas & Mustafa Caglayan, 1996. "Persistence in International Inflation Rates," Boston College Working Papers in Economics 333., Boston College Department of Economics.
  27. repec:hal:journl:peer-00815563 is not listed on IDEAS
  28. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
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