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Modelling long memory volatility in the Bitcoin market: Evidence of persistence and structural breaks

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  • Elie Bouri
  • Luis A. Gil‐Alana
  • Rangan Gupta
  • David Roubaud

Abstract

Motivated by the emergence of Bitcoin as a speculative financial investment, the purpose of this paper is to examine the persistence in the level and volatility of Bitcoin price, accounting for the impact of structural breaks. Using parametric and semiparametric techniques, we find strong evidence in favour of a permanency of the shocks and lack of mean reversion in the level series. We also reveal evidence of structural changes in the dynamics of Bitcoin. After accounting for the structural breaks in the level series, evidence of mean reversion is uncovered in some cases. Further analyses show evidence of a long memory in the two measures of volatility (absolute and the squared returns), whereas some cases of short memory are revealed in the squared returns series in particular. Practical implications are discussed on the inefficiency in the Bitcoin market and its importance for Bitcoin users and investors.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:ijfiec:v:24:y:2019:i:1:p:412-426
    DOI: 10.1002/ijfe.1670
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    References listed on IDEAS

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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. 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.
    3. Pavel Ciaian & Miroslava Rajcaniova & d’Artis Kancs, 2016. "The economics of BitCoin price formation," Applied Economics, Taylor & Francis Journals, vol. 48(19), pages 1799-1815, April.
    4. Jamal Bouoiyour & Refk Selmi & Aviral Kumar Tiwari & Olaolu Richard Olayeni, 2016. "What drives Bitcoin price?," Economics Bulletin, AccessEcon, vol. 36(2), pages 843-850.
    5. Diebold, Francis X. & Rudebusch, Glenn D., 1989. "Long memory and persistence in aggregate output," Journal of Monetary Economics, Elsevier, vol. 24(2), pages 189-209, September.
    6. 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.
    7. Philipp Sibbertsen, 2004. "Long memory in volatilities of German stock returns," Empirical Economics, Springer, vol. 29(3), pages 477-488, September.
    8. Sowell, Fallaw, 1992. "Modeling long-run behavior with the fractional ARIMA model," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 277-302, April.
    9. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
    10. Selgin, George, 2015. "Synthetic commodity money," Journal of Financial Stability, Elsevier, vol. 17(C), pages 92-99.
    11. Jamal Bouoiyour & Refk Selmi, 2015. "What Does Bitcoin Look Like?," Annals of Economics and Finance, Society for AEF, vol. 16(2), pages 449-492, November.
    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. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
    14. Dwyer, Gerald P., 2015. "The economics of Bitcoin and similar private digital currencies," Journal of Financial Stability, Elsevier, vol. 17(C), pages 81-91.
    15. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    16. 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.
    17. Gil-Alana, Luis A. & Moreno, Antonio, 2012. "Uncovering the US term premium: An alternative route," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 1181-1193.
    18. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    19. Jamal Bouoiyour & Refk Selmi & Aviral Kumar Tiwari, 2015. "Is Bitcoin Business Income Or Speculative Foolery? New Ideas Through An Improved Frequency Domain Analysis," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 1-23.
    20. 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.
    21. David Yermack, 2013. "Is Bitcoin a Real Currency? An economic appraisal," NBER Working Papers 19747, National Bureau of Economic Research, Inc.
    22. Efimova, Olga & Serletis, Apostolos, 2014. "Energy markets volatility modelling using GARCH," Energy Economics, Elsevier, vol. 43(C), pages 264-273.
    23. Anne Haubo Dyhrberg, 2015. "Hedging Capabilities of Bitcoin. Is it the virtual gold?," Working Papers 201521, School of Economics, University College Dublin.
    24. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
    25. repec:agr:journl:v:1(590):y:2014:i:1(590):p:103-114 is not listed on IDEAS
    26. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    27. Brandvold, Morten & Molnár, Peter & Vagstad, Kristian & Andreas Valstad, Ole Christian, 2015. "Price discovery on Bitcoin exchanges," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 36(C), pages 18-35.
    28. Cheah, Eng-Tuck & Fry, John, 2015. "Speculative bubbles in Bitcoin markets? An empirical investigation into the fundamental value of Bitcoin," Economics Letters, Elsevier, vol. 130(C), pages 32-36.
    29. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 257-287, August.
    30. Angela ROGOJANU & Liana BADEA, 2014. "The issue of competing currencies. Case study – Bitcoin," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(1(590)), pages 103-114, January.
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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G1 - Financial Economics - - General Financial Markets

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