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Price Appreciation and Roughness Duality in Bitcoin: A Multifractal Analysis

Author

Listed:
  • Cristiana Vaz

    (Department of Mathematics, Faculty of Economics, University of Coimbra, 3004-512 Coimbra, Portugal)

  • Rui Pascoal

    (Centre for Business and Economics Research (CeBER), Faculty of Economics, University of Coimbra, 3004-512 Coimbra, Portugal)

  • Helder Sebastião

    (Centre for Business and Economics Research (CeBER), Faculty of Economics, University of Coimbra, 3004-512 Coimbra, Portugal)

Abstract

Since its launch in 2009, bitcoin has thrived, attracting the attention of investors, regulators, academia, and the public in general. Its price dynamics, characterized by extreme volatility, severe jumps, and impressive long-term appreciation, suggest that bitcoin is a new digital asset. This study presents a comprehensive overview of the fractality of bitcoin in a high-frequency framework, namely by applying Multifractal Detrended Fluctuation Analysis (MF-DFA) and a Multifractal Regime Detecting Method (MRDM) to Bitstamp 1 min bitcoin returns from January 2013 to July 2020. The results suggest that bitcoin is multifractal, with smaller and larger fluctuations being persistent and anti-persistent, respectively. Multifractality comes from significant long-range correlations, which cast some doubts on the informational efficiency at this frequency, but mainly comes from fat-tails, which highlights the significant risks undertaken by investors in this market. Our most important result is that the degree and richness of multifractality is time-varying and increased after 2017, when volumes and prices experienced an explosive behaviour. This complexity puts into perspective the duality of bitcoin: while it is characterized by long-run attractiveness and increasing valuation, it also has a high short-run instability. Hence, this study provides some empirical evidence supporting the relationship between these two observable features.

Suggested Citation

  • Cristiana Vaz & Rui Pascoal & Helder Sebastião, 2021. "Price Appreciation and Roughness Duality in Bitcoin: A Multifractal Analysis," Mathematics, MDPI, vol. 9(17), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2088-:d:624535
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    as
    1. Caporale, Guglielmo Maria & Gil-Alana, Luis & Plastun, Alex, 2018. "Persistence in the cryptocurrency market," Research in International Business and Finance, Elsevier, vol. 46(C), pages 141-148.
    2. Zhang, Wei & Wang, Pengfei & Li, Xiao & Shen, Dehua, 2018. "The inefficiency of cryptocurrency and its cross-correlation with Dow Jones Industrial Average," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 658-670.
    3. Tetsuya Takaishi, 2017. "Statistical properties and multifractality of Bitcoin," Papers 1707.07618, arXiv.org, revised May 2018.
    4. Natália Costa & César Silva & Paulo Ferreira, 2019. "Long-Range Behaviour and Correlation in DFA and DCCA Analysis of Cryptocurrencies," IJFS, MDPI, vol. 7(3), pages 1-12, September.
    5. 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.
    6. Bariviera, Aurelio F. & Basgall, María José & Hasperué, Waldo & Naiouf, Marcelo, 2017. "Some stylized facts of the Bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 82-90.
    7. Fernandes, Leonardo H.S. & Araújo, Fernando H.A. & Silva, Igor E.M. & Leite, Urbanno P.S. & de Lima, Neílson F. & Stosic, Tatijana & Ferreira, Tiago A.E., 2020. "Multifractal behavior in the dynamics of Brazilian inflation indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    8. Josselin Garnier & Knut Solna, 2018. "Chaos and Order in the Bitcoin Market," Papers 1809.08403, arXiv.org, revised Apr 2019.
    9. Kristoufek, Ladislav & Vosvrda, Miloslav, 2016. "Gold, currencies and market efficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 27-34.
    10. Kristjanpoller, Werner & Bouri, Elie, 2019. "Asymmetric multifractal cross-correlations between the main world currencies and the main cryptocurrencies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1057-1071.
    11. Di Matteo, T. & Aste, T. & Dacorogna, M.M., 2003. "Scaling behaviors in differently developed markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 183-188.
    12. Mnif, Emna & Jarboui, Anis & Mouakhar, Khaireddine, 2020. "How the cryptocurrency market has performed during COVID 19? A multifractal analysis," Finance Research Letters, Elsevier, vol. 36(C).
    13. Kristoufek, Ladislav & Vosvrda, Miloslav, 2013. "Measuring capital market efficiency: Global and local correlations structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 184-193.
    14. Jiang, Yonghong & Nie, He & Ruan, Weihua, 2018. "Time-varying long-term memory in Bitcoin market," Finance Research Letters, Elsevier, vol. 25(C), pages 280-284.
    15. Anderson, Nicola & Noss, Joseph, 2013. "Financial Stability Paper No 23: The Fractal Market Hypothesis and its implications for the stability of financial markets," Bank of England Financial Stability Papers 23, Bank of England.
    16. Wang, Yudong & Liu, Li & Gu, Rongbao, 2009. "Analysis of efficiency for Shenzhen stock market based on multifractal detrended fluctuation analysis," International Review of Financial Analysis, Elsevier, vol. 18(5), pages 271-276, December.
    17. da Silva Filho, Antônio Carlos & Maganini, Natália Diniz & de Almeida, Eduardo Fonseca, 2018. "Multifractal analysis of Bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 954-967.
    18. Lim, Gyuchang & Kim, SooYong & Lee, Hyoung & Kim, Kyungsik & Lee, Dong-In, 2007. "Multifractal detrended fluctuation analysis of derivative and spot markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 259-266.
    19. Lahmiri, Salim & Bekiros, Stelios, 2018. "Chaos, randomness and multi-fractality in Bitcoin market," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 28-34.
    20. Helder Sebastião & Pedro Godinho, 2021. "Forecasting and trading cryptocurrencies with machine learning under changing market conditions," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-30, December.
    21. Cheng, Qing & Liu, Xinyuan & Zhu, Xiaowu, 2019. "Cryptocurrency momentum effect: DFA and MF-DFA analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    22. Bariviera, Aurelio F., 2021. "One model is not enough: Heterogeneity in cryptocurrencies’ multifractal profiles," Finance Research Letters, Elsevier, vol. 39(C).
    23. Wang, Yudong & Wei, Yu & Wu, Chongfeng, 2011. "Analysis of the efficiency and multifractality of gold markets based on multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 817-827.
    24. Urquhart, Andrew, 2016. "The inefficiency of Bitcoin," Economics Letters, Elsevier, vol. 148(C), pages 80-82.
    25. Stavroyiannis, Stavros & Babalos, Vassilios & Bekiros, Stelios & Lahmiri, Salim & Uddin, Gazi Salah, 2019. "The high frequency multifractal properties of Bitcoin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 62-71.
    26. Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1997. "Large Deviations and the Distribution of Price Changes," Cowles Foundation Discussion Papers 1165, Cowles Foundation for Research in Economics, Yale University.
    27. Bariviera, Aurelio F., 2017. "The inefficiency of Bitcoin revisited: A dynamic approach," Economics Letters, Elsevier, vol. 161(C), pages 1-4.
    28. Garnier, Josselin & Solna, Knut, 2019. "Chaos and order in the bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 708-721.
    29. Mensi, Walid & Lee, Yun-Jung & Al-Yahyaee, Khamis Hamed & Sensoy, Ahmet & Yoon, Seong-Min, 2019. "Intraday downward/upward multifractality and long memory in Bitcoin and Ethereum markets: An asymmetric multifractal detrended fluctuation analysis," Finance Research Letters, Elsevier, vol. 31(C), pages 19-25.
    30. Lee, Hojin & Chang, Woojin, 2015. "Multifractal regime detecting method for financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 117-129.
    31. 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.
    32. Chuxuan Jiang & Priya Dev & Ross A. Maller, 2020. "A Hypothesis Test Method for Detecting Multifractal Scaling, Applied to Bitcoin Prices," JRFM, MDPI, vol. 13(5), pages 1-21, May.
    33. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2019. "Multifractal behavior of price and volume changes in the cryptocurrency market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 54-61.
    34. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
    35. Takaishi, Tetsuya, 2018. "Statistical properties and multifractality of Bitcoin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 507-519.
    36. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    37. Telli, Şahin & Chen, Hongzhuan, 2020. "Multifractal behavior in return and volatility series of Bitcoin and gold in comparison," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    38. Naeem, Muhammad Abubakr & Bouri, Elie & Peng, Zhe & Shahzad, Syed Jawad Hussain & Vo, Xuan Vinh, 2021. "Asymmetric efficiency of cryptocurrencies during COVID19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    39. Zhang, Xin & Yang, Liansheng & Zhu, Yingming, 2019. "Analysis of multifractal characterization of Bitcoin market based on multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 973-983.
    40. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    41. Fang, Wen & Tian, Shaolin & Wang, Jun, 2018. "Multiscale fluctuations and complexity synchronization of Bitcoin in China and US markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 109-120.
    42. Benoit B. Mandelbrot, 1972. "Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290, National Bureau of Economic Research, Inc.
    43. Sebastião, Helder & Godinho, Pedro, 2020. "Bitcoin futures: An effective tool for hedging cryptocurrencies," Finance Research Letters, Elsevier, vol. 33(C).
    44. Zhang, Yuanyuan & Chan, Stephen & Chu, Jeffrey & Nadarajah, Saralees, 2019. "Stylised facts for high frequency cryptocurrency data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 598-612.
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