[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/diw/diwwpp/dp1294.html
   My bibliography  Save this paper

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

Author

Listed:
  • Guglielmo Maria Caporale
  • Luis A. Gil-Alana
Abstract
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.

Suggested Citation

  • Guglielmo Maria Caporale & Luis A. Gil-Alana, 2013. "Long Memory and Fractional Integration in High Frequency Data on the US Dollar / British Pound Spot Exchange Rate," Discussion Papers of DIW Berlin 1294, DIW Berlin, German Institute for Economic Research.
    • Handle: RePEc:diw:diwwpp:dp1294
    as

    Download full text from publisher

    File URL: https://www.diw.de/documents/publikationen/73/diw_01.c.420510.de/dp1294.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Summers, Lawrence H, 1986. "Does the Stock Market Rationally Reflect Fundamental Values?," Journal of Finance, American Finance Association, vol. 41(3), pages 591-601, July.
    2. 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.
    3. 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.
    4. 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.
    5. Leonardo Rocha Souza, 2008. "Why Aggregate Long Memory Time Series?," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 298-316.
    6. 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.
    7. 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.
    8. Gilles Dufrenot & Laurent Mathieu & Valerie Mignon & Anne Peguin-Feissolle, 2006. "Persistent misalignments of the European exchange rates: some evidence from non-linear cointegration," Applied Economics, Taylor & Francis Journals, vol. 38(2), pages 203-229.
    9. 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.
    10. 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.
    11. Wang, Changyun, 2004. "Futures trading activity and predictable foreign exchange market movements," Journal of Banking & Finance, Elsevier, vol. 28(5), pages 1023-1041, May.
    12. Philipp Sibbertsen, 2004. "Long memory in volatilities of German stock returns," Empirical Economics, Springer, vol. 29(3), pages 477-488, September.
    13. Leonardo Rocha Souza, 2005. "A Note On Chambers'S "Long Memory And Aggregation In Macroeconomic Time Series"," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(3), pages 1059-1062, August.
    14. 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.
    15. Aloy, Marcel & Boutahar, Mohamed & Gente, Karine & Péguin-Feissolle, Anne, 2011. "Purchasing power parity and the long memory properties of real exchange rates: Does one size fit all?," Economic Modelling, Elsevier, vol. 28(3), pages 1279-1290, May.
    16. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
    17. Dufrénot, Gilles & Lardic, Sandrine & Mathieu, Laurent & Mignon, Valérie & Péguin-Feissolle, Anne, 2008. "Explaining the European exchange rates deviations: Long memory or non-linear adjustment?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 18(3), pages 207-215, July.
    18. Guglielmo Maria Caporale & Juncal Cuñado & Luis A. Gil-Alana, 2013. "Modelling long-run trends and cycles in financial time series data," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 405-421, May.
    19. Gil-Alana, Luis A., 2000. "Mean reversion in the real exchange rates," Economics Letters, Elsevier, vol. 69(3), pages 285-288, December.
    20. repec:hal:journl:peer-00815563 is not listed on IDEAS
    21. Guglielmo Maria Caporale & Luis Gil‐Alana, 2014. "Long‐Run and Cyclical Dynamics in the US Stock Market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(2), pages 147-161, March.
    22. 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.
    23. 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.
    24. Leonardo Rocha Souza, 2007. "Temporal Aggregation and Bandwidth selection in estimating long memory," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(5), pages 701-722, September.
    25. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    26. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
    27. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    28. 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.
    29. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
    30. 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.
    31. Ignacio N Lobato & Carlos Velasco, 2007. "Efficient Wald Tests for Fractional Unit Roots," Econometrica, Econometric Society, vol. 75(2), pages 575-589, March.
    32. Demetrescu, Matei & Kuzin, Vladimir & Hassler, Uwe, 2008. "Long Memory Testing In The Time Domain," Econometric Theory, Cambridge University Press, vol. 24(1), pages 176-215, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Luis A. Gil-Alana & Christophe André & Rangan Gupta & Tsangyao Chang & Omid Ranjbar, 2016. "The Feldstein--Horioka puzzle in South Africa: A fractional cointegration approach," The Journal of International Trade & Economic Development, Taylor & Francis Journals, vol. 25(7), pages 978-991, October.
    2. Gil-Alana, Luis A. & Infante, Juan & Martín-Valmayor, Miguel Angel, 2023. "Persistence and long run co-movements across stock market prices," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 347-357.
    3. Proelss, Juliane & Schweizer, Denis & Seiler, Volker, 2020. "The economic importance of rare earth elements volatility forecasts," International Review of Financial Analysis, Elsevier, vol. 71(C).
    4. Hadhri, Sinda & Ftiti, Zied, 2019. "Commonality in liquidity among Middle East and North Africa emerging stock markets: Does it really matter?," Economic Systems, Elsevier, vol. 43(3).
    5. Giorgio Canarella & Luis A. Gil-Alana & Rangan Gupta & Stephen M. Miller, 2020. "Modeling US historical time-series prices and inflation using alternative long-memory approaches," Empirical Economics, Springer, vol. 58(4), pages 1491-1511, April.
    6. Matthieu Garcin, 2019. "Hurst Exponents And Delampertized Fractional Brownian Motions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-26, August.
    7. Shi, Yanlin & Ho, Kin-Yip, 2015. "Modeling high-frequency volatility with three-state FIGARCH models," Economic Modelling, Elsevier, vol. 51(C), pages 473-483.
    8. Slim Chaouachi & Zied Ftiti & Frederic Teulon, 2014. "Explaining the Tunisian Real Exchange: Long Memory versus Structural Breaks," Working Papers 2014-147, Department of Research, Ipag Business School.
    9. Zied Ftiti & Slim Chaouachi, 2018. "What Can We Learn About the Real Exchange Rate Behavior in the Case of a Peripheral Country?," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 16(3), pages 681-707, September.
    10. Lujia Bai & Weichi Wu, 2021. "Detecting long-range dependence for time-varying linear models," Papers 2110.08089, arXiv.org, revised Mar 2023.
    11. Guglielmo Maria Caporale & Alex Plastun, 2022. "Persistence in High Frequency Financial Data," CESifo Working Paper Series 10045, CESifo.
    12. Sankarkumar, Amirdha Vasani & Selvam, Murugesan & Maniam, Balasundram & Sigo, Marxia Oli, 2017. "Long memory features and relationship stability of Asia-Pacific currencies against USD," Business and Economic Horizons (BEH), Prague Development Center (PRADEC), vol. 13(1).
    13. Gao, Guangyuan & Ho, Kin-Yip & Shi, Yanlin, 2020. "Long memory or regime switching in volatility? Evidence from high-frequency returns on the U.S. stock indices," Pacific-Basin Finance Journal, Elsevier, vol. 61(C).
    14. Mensi, Walid & Hammoudeh, Shawkat & Yoon, Seong-Min, 2014. "Structural breaks and long memory in modeling and forecasting volatility of foreign exchange markets of oil exporters: The importance of scheduled and unscheduled news announcements," International Review of Economics & Finance, Elsevier, vol. 30(C), pages 101-119.
    15. Matthieu Garcin, 2018. "Hurst exponents and delampertized fractional Brownian motions," Working Papers hal-01919754, HAL.
    16. Giorgio Canarella & Luis A. Gil-Alana & Rangan Gupta & Stephen M. Miller, 2016. "Modeling U.S. Historical Time-Series Prices and Inflation Using Various Linear and Nonlinear Long-Memory Approaches," Working Papers 201683, University of Pretoria, Department of Economics.
    17. Shi, Yanlin & Ho, Kin-Yip, 2015. "Long memory and regime switching: A simulation study on the Markov regime-switching ARFIMA model," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 189-204.
    18. repec:ipg:wpaper:2014-390 is not listed on IDEAS
    19. Omane-Adjepong, Maurice & Boako, Gidoen & Alagidede, Paul, 2018. "Modelling heterogeneous speculation in Ghana’s foreign exchange market: Evidence from ARFIMA-FIGARCH and Semi-Parametric methods," MPRA Paper 86617, University Library of Munich, Germany.
    20. Joseph Mawejje & Ezra Francis Munyambonera, 2016. "Tax Revenue Effects of Sectoral Growth and Public Expenditure in Uganda," South African Journal of Economics, Economic Society of South Africa, vol. 84(4), pages 538-554, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2011. "Long Memory and Fractional Integration in High-Frequency British Pound / Dollar Spot Exchange Rates," Faculty Working Papers 02/11, School of Economics and Business Administration, University of Navarra.
    2. Luis A. Gil-Alana & Yun Cao, 2011. "Stock market prices in China. Efficiency, mean reversion, long memory volatility and other implicit dynamics," Faculty Working Papers 12/11, School of Economics and Business Administration, University of Navarra.
    3. 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.
    4. Luis A. Gil‐Alana & Robert Mudida & OlaOluwa S. Yaya & Kazeem A. Osuolale & Ahamuefula E. Ogbonna, 2021. "Mapping US presidential terms with S&P500 index: Time series analysis approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 1938-1954, April.
    5. Carlos P. Barros & Luis A. Gil-Alana & Zhongfei Chen, 2016. "Exchange rate persistence of the Chinese yuan against the US dollar in the NDF market," Empirical Economics, Springer, vol. 51(4), pages 1399-1414, December.
    6. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    7. Guglielmo Maria Caporale & Luis Gil-Alana, 2011. "The weekly structure of US stock prices," Applied Financial Economics, Taylor & Francis Journals, vol. 21(23), pages 1757-1764.
    8. Luis Alberiko & OlaOluwa S. Yaya & Olarenwaju I. Shittu, 2015. "Fractional integration and asymmetric volatility in european, asian and american bull and bear markets. Applications to high frequency stock data," NCID Working Papers 07/2015, Navarra Center for International Development, University of Navarra.
    9. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.
    10. Gil-Alana, Luis A. & Mudida, Robert & Yaya, OlaOluwa S & Osuolale, Kazeem & Ogbonna, Ephraim A, 2019. "Influence of US Presidential Terms on S&P500 Index Using a Time Series Analysis Approach," MPRA Paper 93941, University Library of Munich, Germany.
    11. Alia Afzal & Philipp Sibbertsen, 2021. "Modeling fractional cointegration between high and low stock prices in Asian countries," Empirical Economics, Springer, vol. 60(2), pages 661-682, February.
    12. Gil-Alana, Luis A. & Shittu, Olanrewaju I. & Yaya, OlaOluwa S., 2014. "On the persistence and volatility in European, American and Asian stocks bull and bear markets," Journal of International Money and Finance, Elsevier, vol. 40(C), pages 149-162.
    13. Monge, Manuel & Gil-Alana, Luis A. & Pérez de Gracia, Fernando, 2017. "Crude oil price behaviour before and after military conflicts and geopolitical events," Energy, Elsevier, vol. 120(C), pages 79-91.
    14. J. Cuñado & L. Gil-Alana & F. Gracia, 2009. "US stock market volatility persistence: evidence before and after the burst of the IT bubble," Review of Quantitative Finance and Accounting, Springer, vol. 33(3), pages 233-252, October.
    15. Bhandari, Avishek, 2020. "Long memory and fractality among global equity markets: A multivariate wavelet approach," MPRA Paper 99653, University Library of Munich, Germany.
    16. Carlos Barros & Guglielmo Maria Caporale & Luis Gil-Alana, 2014. "Long Memory in Angolan Macroeconomic Series: Mean Reversion versus Explosive Behaviour," African Development Review, African Development Bank, vol. 26(1), pages 59-73.
    17. Steven Clark & T. Coggin, 2011. "Are U.S. stock prices mean reverting? Some new tests using fractional integration models with overlapping data and structural breaks," Empirical Economics, Springer, vol. 40(2), pages 373-391, April.
    18. Guglielmo Maria Caporale & Luis Gil-Alana, 2004. "Long range dependence in daily stock returns," Applied Financial Economics, Taylor & Francis Journals, vol. 14(6), pages 375-383.
    19. Elie Bouri & Luis A. Gil‐Alana & Rangan Gupta & David Roubaud, 2019. "Modelling long memory volatility in the Bitcoin market: Evidence of persistence and structural breaks," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 24(1), pages 412-426, January.
    20. Geoffrey Ngene & Ann Nduati Mungai & Allen K. Lynch, 2018. "Long-Term Dependency Structure and Structural Breaks: Evidence from the U.S. Sector Returns and Volatility," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-38, June.

    More about this item

    Keywords

    High frequency data; long memory; volatility persistence; structural breaks;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • F31 - International Economics - - International Finance - - - Foreign Exchange

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:diw:diwwpp:dp1294. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Bibliothek (email available below). General contact details of provider: https://edirc.repec.org/data/diwbede.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.