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Long Memory and Volatility Dynamics in the US Dollar Exchange Rate

Author

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  • Guglielmo Maria Caporale

    (Brunel University, UK)

  • Luis Gil-Alana

    (University of Navarra, Spain)

Abstract

This paper focuses on nominal exchange rates, specifically the US dollar rate vis-a-vis the Euro and the Japanese Yen at a daily frequency. In the paper both absolute values of returns and squared returns are modelled using long-memory techniques, being particularly interested in volatility modelling and forecasting. Compared with previous studies using fractional integration such as Granger and Ding (1996), a more general model is estimated, 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(1) model seem to be the most appropriate for the US dollar rate vis-a-vis the Euro and the Japanese Yen respectively.

Suggested Citation

  • Guglielmo Maria Caporale & Luis Gil-Alana, 2012. "Long Memory and Volatility Dynamics in the US Dollar Exchange Rate," Multinational Finance Journal, Multinational Finance Journal, vol. 16(1-2), pages 105-136, March - J.
  • Handle: RePEc:mfj:journl:v:16:y:2012:i:1-2:p:105-136
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    1. 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.
    2. Henry L. Gray & Nien‐Fan Zhang & Wayne A. Woodward, 1994. "On Generalized Fractional Processes – A Correction," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 561-562, September.
    3. Carlos Velasco, 1999. "Gaussian Semiparametric Estimation of Non‐stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(1), pages 87-127, January.
    4. Wang, Changyun, 2004. "Futures trading activity and predictable foreign exchange market movements," Journal of Banking & Finance, Elsevier, vol. 28(5), pages 1023-1041, May.
    5. Philipp Sibbertsen, 2004. "Long memory in volatilities of German stock returns," Empirical Economics, Springer, vol. 29(3), pages 477-488, September.
    6. Andersen, Torben G & Bollerslev, Tim, 1997. "Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July.
    7. Dalla, Violetta & Hidalgo, Javier, 2005. "A parametric bootstrap test for cycles," LSE Research Online Documents on Economics 6829, London School of Economics and Political Science, LSE Library.
    8. Christopher F. Baum & John T. Barkoulas & Mustafa Caglayan, 1999. "Persistence in International Inflation Rates," Southern Economic Journal, John Wiley & Sons, vol. 65(4), pages 900-913, April.
    9. 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 261-268, July.
    10. Richard T. Baillie & Aydin A. Cecen & Young-Wook Han, 2000. "High Frequency Deutsche Mark-US Dollar Returns: FIGARCH Representations and Non Linearities," Multinational Finance Journal, Multinational Finance Journal, vol. 4(3-4), pages 247-267, September.
    11. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    12. Luis A. Gil‐Alana, 2008. "Fractional integration and structural breaks at unknown periods of time," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 163-185, January.
    13. Tsay, Wen-Jen & Härdle, Wolfgang Karl, 2007. "A generalized ARFIMA process with Markov-switching fractional differencing parameter," SFB 649 Discussion Papers 2007-022, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    14. 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.
    15. 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.
    16. 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.
    17. Cheung, Yin-Wong & Lai, Kon S., 1994. "Mean reversion in real exchange rates," Economics Letters, Elsevier, vol. 46(3), pages 251-256, November.
    18. Chung, Ching-Fan, 1996. "Estimating a generalized long memory process," Journal of Econometrics, Elsevier, vol. 73(1), pages 237-259, July.
    19. Lothian, James R. & Taylor, Mark P., 1997. "Real exchange rate behavior," Journal of International Money and Finance, Elsevier, vol. 16(6), pages 945-954, December.
    20. 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.
    21. Violetta Dalla & Javier Hidalgo, 2005. "A Parametric Bootstrap Test for Cycles," STICERD - Econometrics Paper Series 486, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    22. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    23. Ching‐Fan Chung, 1996. "A Generalized Fractionally Integrated Autoregressive Moving‐Average Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(2), pages 111-140, March.
    24. Hsing Fang & Kon S. Lai & Michael Lai, 1994. "Fractal structure in currency futures price dynamics," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 14(2), pages 169-181, April.
    25. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
    26. Nuno Crato & Bonnie K. Ray, 2000. "Memory in returns and volatilities of futures' contracts," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 20(6), pages 525-543, July.
    27. Dalla, Violetta & Hidalgo, Javier, 2005. "A parametric bootstrap test for cycles," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 219-261.
    28. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    29. Lothian, James R & Taylor, Mark P, 1996. "Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 488-509, June.
    30. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
    31. 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 280-283, July.
    32. Henry L. Gray & Nien‐Fan Zhang & Wayne A. Woodward, 1989. "On Generalized Fractional Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(3), pages 233-257, May.
    33. Booth, G. Geoffrey & Kaen, Fred R. & Koveos, Peter E., 1982. "R/S analysis of foreign exchange rates under two international monetary regimes," Journal of Monetary Economics, Elsevier, vol. 10(3), pages 407-415.
    34. 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.
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    Cited by:

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    2. 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.
    3. 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.
    4. Rania Jammazi & Chaker Aloui, 2014. "Cyclical components and dual long memory in the foreign exchange rate dynamics: the Tunisian case," Working Papers 2014-198, Department of Research, Ipag Business School.

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    More about this item

    Keywords

    Fractional integration; Long memory; Exchange rates; Volatility;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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