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Long memory and efficiency of Bitcoin under heavy tails

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  • Liang Wu
  • Shujuan Chen

Abstract

The long memory is usually defined via auto-covariances which further connect with Hurst exponent. The heavy tails in Bitcoin returns can cause infinite auto-covariances which make the analysis of long memory and market efficiency in Bitcoin based on estimation of Hurst exponent inappropriate. Few literatures focus on this problem. We provide two approaches based on shuffling method and rank-ordered technique to this problem, and further combine them to analyse the time-varying efficiency and long memory in Bitcoin using sliding window. Results show that the inefficiency and long memory exist in Bitcoin before 2014 and after mid-2017. Especially, the latest data reveal a recent new change that the Bitcoin market has become inefficient and exhibited long memory behaviour since mid-2017, but is turning back to efficiency recently. This change may be due to the frequent key events of Bitcoin in 2017 and 2018, which can break the weak efficiency of Bitcoin. The heavy negative tails with $$\alpha \lt 2$$α

Suggested Citation

  • Liang Wu & Shujuan Chen, 2020. "Long memory and efficiency of Bitcoin under heavy tails," Applied Economics, Taylor & Francis Journals, vol. 52(48), pages 5298-5309, October.
    • Handle: RePEc:taf:applec:v:52:y:2020:i:48:p:5298-5309
    DOI: 10.1080/00036846.2020.1761942
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    Cited by:

    1. Apostolakis, George N., 2024. "Bitcoin price volatility transmission between spot and futures markets," International Review of Financial Analysis, Elsevier, vol. 94(C).
    2. Grobys, Klaus, 2023. "A Fractal and Comparative View of the Memory of Bitcoin and S&P 500 Returns," Research in International Business and Finance, Elsevier, vol. 66(C).
    3. Iraj Daizadeh, 2021. "Leveraging latent persistency in United States patent and trademark applications to gain insight into the evolution of an innovation-driven economy," Papers 2101.02588, arXiv.org, revised May 2021.
    4. Andrew Phiri, 2022. "Can wavelets produce a clearer picture of weak-form market efficiency in Bitcoin?," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 12(3), pages 373-386, September.
    5. Ahmed, Walid M.A., 2021. "Stock market reactions to upside and downside volatility of Bitcoin: A quantile analysis," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    6. Assaf, Ata & Mokni, Khaled & Yousaf, Imran & Bhandari, Avishek, 2023. "Long memory in the high frequency cryptocurrency markets using fractal connectivity analysis: The impact of COVID-19," Research in International Business and Finance, Elsevier, vol. 64(C).
    7. Manahov, Viktor & Urquhart, Andrew, 2021. "The efficiency of Bitcoin: A strongly typed genetic programming approach to smart electronic Bitcoin markets," International Review of Financial Analysis, Elsevier, vol. 73(C).
    8. Cao, Guangxi & Ling, Meijun, 2022. "Asymmetry and conduction direction of the interdependent structure between cryptocurrency and US dollar, renminbi, and gold markets," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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