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

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  • 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
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    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.

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    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

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