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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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    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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