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Long Memory and Volatility Dynamics in the US Dollar Exchange Rate

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  • Guglielmo Maria Caporale
  • Luis A. Gil-Alana

Abstract

This paper focuses on nominal exchange rates, specifically the US dollar rate vis-à-vis the Euro and the Japanese Yen at a daily frequency. We model both absolute values of returns and squared returns using long-memory techniques, being particularly interested in volatility modelling and forecasting given their importance for FOREX dealers. Compared with previous studies using a standard fractional integration framework such as Granger and Ding (1996), we estimate a more general model which allows for dependence not only at the zero but also at other frequencies. The results show differences in the behaviour of the two series: a long-memory cyclical model and a standard I(d) model seem to be the most appropriate for the US dollar rate vis-à-vis the Euro and the Japanese Yen respectively.

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File URL: http://www.diw.de/documents/publikationen/73/diw_01.c.347170.de/dp975.pdf
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Bibliographic Info

Paper provided by DIW Berlin, German Institute for Economic Research in its series Discussion Papers of DIW Berlin with number 975.

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Length: 37 p.
Date of creation: 2010
Date of revision:
Handle: RePEc:diw:diwwpp:dp975

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Keywords: Fractional integration; Long memory; Exchange rates; Volatility;

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References

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  1. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 261-68, July.
  2. Wen-Jen Tsay & Wolfgang Härdle, 2007. "A Generalized ARFIMA Process with Markov-Switching Fractional Differencing Parameter," SFB 649 Discussion Papers SFB649DP2007-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. Sibbertsen, Philipp, 2001. "Long-memory in volatilities of German stock returns," Technical Reports 2001,42, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  4. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Cowles Foundation Discussion Papers 1367, Cowles Foundation for Research in Economics, Yale University, revised Jul 2004.
  5. Wang, Changyun, 2004. "Futures trading activity and predictable foreign exchange market movements," Journal of Banking & Finance, Elsevier, vol. 28(5), pages 1023-1041, May.
  6. Luis A. Gil-Alana, . "Fractional integration and structural breaks at unknown periods of time," Faculty Working Papers 16/06, School of Economics and Business Administration, University of Navarra.
  7. Violetta Dalla & Javier Hidalgo, 2005. "A Parametric Bootstrap Test for Cycles," STICERD - Econometrics Paper Series /2005/486, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  8. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  9. John Cotter, 2005. "Uncovering long memory in high frequency UK futures," The European Journal of Finance, Taylor & Francis Journals, vol. 11(4), pages 325-337.
  10. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
  11. Torben G. Andersen & Tim Bollerslev, 1996. "Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," NBER Working Papers 5752, National Bureau of Economic Research, Inc.
  12. 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.
  13. 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.
  14. Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Local Whittle Estimation in Nonstationary and Unit Root Cases," Cowles Foundation Discussion Papers 1266, Cowles Foundation for Research in Economics, Yale University, revised Sep 2003.
  15. Chung, Ching-Fan, 1996. "Estimating a generalized long memory process," Journal of Econometrics, Elsevier, vol. 73(1), pages 237-259, July.
  16. Morana, Claudio & Beltratti, Andrea, 2004. "Structural change and long-range dependence in volatility of exchange rates: either, neither or both?," Journal of Empirical Finance, Elsevier, vol. 11(5), pages 629-658, December.
  17. Ferrara, Laurent & Guegan, Dominique, 2001. "Forecasting with k-Factor Gegenbauer Processes: Theory and Applications," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(8), pages 581-601, December.
  18. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
  19. Cheung, Yin-Wong, 1993. "Long Memory in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 93-101, January.
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Cited by:
  1. Trenca Ioan & Cociuba Mihail Ioan, 2011. "Modeling Romanian Exchange Rate Evolution With Garch, Tgarch, Garch- In Mean Models," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(special), pages 299-305, July.
  2. Bruno Versailles, 2012. "Market Intergration and Border Effects in Eastern Africa," CSAE Working Paper Series 2012-01, Centre for the Study of African Economies, University of Oxford.

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