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Long range dependence in the Bitcoin market: A study based on high-frequency data

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  • Zargar, Faisal Nazir
  • Kumar, Dilip

Abstract

Using the high-frequency data of Bitcoin, this paper investigates the long memory characteristics of the unconditional and conditional volatilities of Bitcoin at different time scales using the local Whittle (LW) estimator, the exact local Whittle (ELW) estimator and the ARMA–FIAPARCHmodel. The results show that the long memory parameter is significant and quite stable for both unconditional and conditional volatility measures across different time scales. This paper also examines the long memory characteristics of the unconditional and conditional “realized” volatilities of Bitcoin at different time scales using the local Whittle (LW) estimator, exact local Whittle (ELW) estimator and the ARFIMA model. Long memory is found to be significant and stable also in case of unconditional and conditional “realized” volatilities. The study also undertakes quarterly non-overlapping rolling window analysis to develop deeper insights into the evolution of long memory parameter, d, over the period. The results indicate high persistence in the Bitcoin market. This study has useful implications for different investors and market participants having varying exposures in the Bitcoin market depending on their trading horizons. The findings can help them in forecasting the expected volatility in the Bitcoin market and thereby in developing and implementing trading strategies.

Suggested Citation

  • Zargar, Faisal Nazir & Kumar, Dilip, 2019. "Long range dependence in the Bitcoin market: A study based on high-frequency data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 625-640.
    • Handle: RePEc:eee:phsmap:v:515:y:2019:i:c:p:625-640
    DOI: 10.1016/j.physa.2018.09.188
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    1. David Garcia & Claudio Juan Tessone & Pavlin Mavrodiev & Nicolas Perony, 2014. "The digital traces of bubbles: feedback cycles between socio-economic signals in the Bitcoin economy," Papers 1408.1494, arXiv.org.
    2. 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.
    3. Jamal Bouoiyour & Refk Selmi & Aviral Kumar Tiwari & Olaolu Richard Olayeni, 2016. "What drives Bitcoin price?," Economics Bulletin, AccessEcon, vol. 36(2), pages 843-850.
    4. Tiwari, Aviral Kumar & Jana, R.K. & Das, Debojyoti & Roubaud, David, 2018. "Informational efficiency of Bitcoin—An extension," Economics Letters, Elsevier, vol. 163(C), pages 106-109.
    5. repec:agr:journl:v:1(590):y:2014:i:1(590):p:103-114 is not listed on IDEAS
    6. Clifford M. Hurvich & Bonnie K. Ray, 1995. "Estimation Of The Memory Parameter For Nonstationary Or Noninvertible Fractionally Integrated Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(1), pages 17-41, January.
    7. Anton Badev & Matthew Chen, 2014. "Bitcoin: Technical Background and Data Analysis," Finance and Economics Discussion Series 2014-104, Board of Governors of the Federal Reserve System (U.S.).
    8. Urquhart, Andrew, 2016. "The inefficiency of Bitcoin," Economics Letters, Elsevier, vol. 148(C), pages 80-82.
    9. Bariviera, Aurelio F., 2017. "The inefficiency of Bitcoin revisited: A dynamic approach," Economics Letters, Elsevier, vol. 161(C), pages 1-4.
    10. David Garcia & Claudio Tessone & Pavlin Mavrodiev & Nicolas Perony, "undated". "The digital traces of bubbles: feedback cycles between socio-economic signals in the Bitcoin economy," Working Papers ETH-RC-14-001, ETH Zurich, Chair of Systems Design.
    11. Kristoufek, Ladislav, 2018. "On Bitcoin markets (in)efficiency and its evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 257-262.
    12. Thomas Kim, 2015. "The Predecessors of Bitcoin and Their Implications for the Prospect of Virtual Currencies," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-18, April.
    13. 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.
    14. Conrad, Christian & Karanasos, Menelaos & Zeng, Ning, 2011. "Multivariate fractionally integrated APARCH modeling of stock market volatility: A multi-country study," Journal of Empirical Finance, Elsevier, vol. 18(1), pages 147-159, January.
    15. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
    16. Nadarajah, Saralees & Chu, Jeffrey, 2017. "On the inefficiency of Bitcoin," Economics Letters, Elsevier, vol. 150(C), pages 6-9.
    17. Stefan Bornholdt & Kim Sneppen, 2014. "Do Bitcoins make the world go round? On the dynamics of competing crypto-currencies," Papers 1403.6378, arXiv.org.
    18. Dyhrberg, Anne Haubo, 2016. "Bitcoin, gold and the dollar – A GARCH volatility analysis," Finance Research Letters, Elsevier, vol. 16(C), pages 85-92.
    19. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
    20. Fry, John & Cheah, Eng-Tuck, 2016. "Negative bubbles and shocks in cryptocurrency markets," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 343-352.
    21. 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.
    22. Kumar, Dilip, 2014. "Long range dependence in the high frequency USD/INR exchange rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 134-148.
    23. Y. K. Tse, 1998. "The conditional heteroscedasticity of the yen-dollar exchange rate," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(1), pages 49-55.
    24. Angela ROGOJANU & Liana BADEA, 2014. "The issue of competing currencies. Case study – Bitcoin," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(1(590)), pages 103-114, January.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

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    4. Matthias Schnaubelt & Jonas Rende & Christopher Krauss, 2019. "Testing Stylized Facts of Bitcoin Limit Order Books," JRFM, MDPI, vol. 12(1), pages 1-30, February.
    5. Walid Chkili, 2021. "Modeling Bitcoin price volatility: long memory vs Markov switching," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 11(3), pages 433-448, September.
    6. T. Takaishi, 2021. "Power-Law Return-Volatility Cross Correlations of Bitcoin," Papers 2102.08187, arXiv.org.
    7. Nikolaos A. Kyriazis, 2019. "A Survey on Efficiency and Profitable Trading Opportunities in Cryptocurrency Markets," JRFM, MDPI, vol. 12(2), pages 1-17, April.
    8. Wu, Chuanzhen, 2021. "Window effect with Markov-switching GARCH model in cryptocurrency market," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. Chaim, Pedro & Laurini, Márcio P., 2019. "Nonlinear dependence in cryptocurrency markets," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 32-47.
    10. Constandina Koki & Stefanos Leonardos & Georgios Piliouras, 2019. "A Peek into the Unobservable: Hidden States and Bayesian Inference for the Bitcoin and Ether Price Series," Papers 1909.10957, arXiv.org, revised Jul 2021.

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