IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v165y2022ip2s0960077922009857.html
   My bibliography  Save this article

The chaotic, self-similar and hierarchical patterns in Bitcoin and Ethereum price series

Author

Listed:
  • Partida, Alberto
  • Gerassis, Saki
  • Criado, Regino
  • Romance, Miguel
  • Giráldez, Eduardo
  • Taboada, Javier

Abstract

Bitcoin (BTC) and Ethereum (ETH), pioneering public blockchains implementations, are two fundamental levers to register and transfer digital value. This article studies the structure of their daily price volatility time series following a multifaceted approach: first, it examines the existence of chaoticity and fractality in the time series. Obtained results confirm that the BTC and ETH price volatility series present signs of chaoticity, persistence of a long-term correlation and multifractality. Second, it analyses the corresponding visibility graphs associated with these time series using complex network theory. The undirected and connected complex networks, spawned by their natural visibility graphs (VGs) and horizontal visibility graphs (HVGs), present a hierarchical structure. These networks, especially the HVGs, confirm the fractality of the originating time series. The study of HVGs also confirms a lack of uncorrelated randomness in the originating BTC and ETH price series. This paper validates the value of visibility graphs as useful proxies to better understand complex time series, in this case, related to public blockchain implementations.

Suggested Citation

  • Partida, Alberto & Gerassis, Saki & Criado, Regino & Romance, Miguel & Giráldez, Eduardo & Taboada, Javier, 2022. "The chaotic, self-similar and hierarchical patterns in Bitcoin and Ethereum price series," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922009857
    DOI: 10.1016/j.chaos.2022.112806
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922009857
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112806?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Rémy Chicheportiche & Jean-Philippe Bouchaud, 2011. "Goodness-of-Fit tests with Dependent Observations," Post-Print hal-00621061, HAL.
    2. Antoniou, Antonios & Koutmos, Gregory & Pericli, Andreas, 2005. "Index futures and positive feedback trading: evidence from major stock exchanges," Journal of Empirical Finance, Elsevier, vol. 12(2), pages 219-238, March.
    3. Anna D. Broido & Aaron Clauset, 2019. "Scale-free networks are rare," Nature Communications, Nature, vol. 10(1), pages 1-10, December.
    4. Alvarez-Ramirez, Jose & Rodriguez, Eduardo, 2021. "A singular value decomposition approach for testing the efficiency of Bitcoin and Ethereum markets," Economics Letters, Elsevier, vol. 206(C).
    5. Jeff Alstott & Ed Bullmore & Dietmar Plenz, 2014. "powerlaw: A Python Package for Analysis of Heavy-Tailed Distributions," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-11, January.
    6. Remy Chicheportiche & Jean-Philippe Bouchaud, 2011. "Goodness-of-Fit tests with Dependent Observations," Papers 1106.3016, arXiv.org, revised Aug 2011.
    7. Lahmiri, Salim & Bekiros, Stelios, 2018. "Chaos, randomness and multi-fractality in Bitcoin market," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 28-34.
    8. Liu, Keshi & Weng, Tongfeng & Gu, Changgui & Yang, Huijie, 2020. "Visibility graph analysis of Bitcoin price series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    9. Warren E. Weber, 2016. "A Bitcoin Standard: Lessons from the Gold Standard," Staff Working Papers 16-14, Bank of Canada.
    10. Bildirici, Melike E. & Sonustun, Bahri, 2021. "Chaotic behavior in gold, silver, copper and bitcoin prices," Resources Policy, Elsevier, vol. 74(C).
    11. Huang, Jingjing & Shang, Pengjian, 2015. "Multiscale multifractal diffusion entropy analysis of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 221-228.
    12. Cai, Shi-Min & Zhou, Pei-Ling & Yang, Hui-Jie & Yang, Chun-Xia & Wang, Bing-Hong & Zhou, Tao, 2006. "Diffusion entropy analysis on the scaling behavior of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 337-344.
    13. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    14. Xie, Wen-Jie & Zhou, Wei-Xing, 2011. "Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus the Hurst index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3592-3601.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yazıcı, Ali Fırat & Olcay, Ali Bahadır & Arkalı Olcay, Gökçen, 2023. "A framework for maintaining sustainable energy use in Bitcoin mining through switching efficient mining hardware," Technological Forecasting and Social Change, Elsevier, vol. 190(C).
    2. Liu, Hao-Ran & Li, Ming-Xia & Zhou, Wei-Xing, 2024. "Visibility graph analysis of the grains and oilseeds indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 650(C).
    3. Contreras-Aso, Gonzalo & Criado, Regino & Vera de Salas, Guillermo & Yang, Jinling, 2023. "Detecting communities in higher-order networks by using their derivative graphs," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vance Martin & Yoshihiko Nishiyama & John Stachurski, 2011. "A Goodness of Fit Test for Ergodic Markov Processes," ANU Working Papers in Economics and Econometrics 2011-557, Australian National University, College of Business and Economics, School of Economics.
    2. Meng, Xiangyi & Zhou, Bin, 2023. "Scale-free networks beyond power-law degree distribution," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    3. Michele Caraglio & Fulvio Baldovin & Attilio L. Stella, 2021. "How Fast Does the Clock of Finance Run?—A Time-Definition Enforcing Stationarity and Quantifying Overnight Duration," JRFM, MDPI, vol. 14(8), pages 1-15, August.
    4. Morales, Raffaello & Di Matteo, T. & Gramatica, Ruggero & Aste, Tomaso, 2012. "Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3180-3189.
    5. Liu, Hao-Ran & Li, Ming-Xia & Zhou, Wei-Xing, 2024. "Visibility graph analysis of the grains and oilseeds indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 650(C).
    6. B. Zhang & J. Wang & W. Zhang & G. C. Wang, 2020. "Nonlinear Scaling Behavior of Visible Volatility Duration for Financial Statistical Physics Dynamics," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 373-389, August.
    7. Davide Provenzano & Rodolfo Baggio, 2021. "Complexity traits and synchrony of cryptocurrencies price dynamics," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 941-955, December.
    8. Zhang, Hong & Wu, Zheyang, 2022. "The general goodness-of-fit tests for correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    9. Zhou, Yuan-Wu & Liu, Jin-Long & Yu, Zu-Guo & Zhao, Zhi-Qin & Anh, Vo, 2014. "Fractal and complex network analyses of protein molecular dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 21-32.
    10. Dangxing Chen, 2019. "Does the leverage effect affect the return distribution?," Papers 1909.08662, arXiv.org, revised Sep 2019.
    11. Bin Zhou & Petter Holme & Zaiwu Gong & Choujun Zhan & Yao Huang & Xin Lu & Xiangyi Meng, 2023. "The nature and nurture of network evolution," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    12. Mao, Jin & Liang, Zhentao & Cao, Yujie & Li, Gang, 2020. "Quantifying cross-disciplinary knowledge flow from the perspective of content: Introducing an approach based on knowledge memes," Journal of Informetrics, Elsevier, vol. 14(4).
    13. Jean-Philippe Bouchaud, 2021. "Radical Complexity," Papers 2103.09692, arXiv.org.
    14. Alex D Washburne & Joshua W Burby & Daniel Lacker, 2016. "Novel Covariance-Based Neutrality Test of Time-Series Data Reveals Asymmetries in Ecological and Economic Systems," PLOS Computational Biology, Public Library of Science, vol. 12(9), pages 1-14, September.
    15. Chicheportiche, Rémy & Chakraborti, Anirban, 2017. "A model-free characterization of recurrences in stationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 312-318.
    16. Yonghong Jin & Qi Zhang & Lifei Shan & Sai-Ping Li, 2015. "Characteristics of Venture Capital Network and Its Correlation with Regional Economy: Evidence from China," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-20, September.
    17. Christie Smith & Aaron Kumar, 2018. "Crypto‐Currencies – An Introduction To Not‐So‐Funny Moneys," Journal of Economic Surveys, Wiley Blackwell, vol. 32(5), pages 1531-1559, December.
    18. Angelidis, Dimitrios & Koulakiotis Athanasios & Kiohos Apostolos, 2018. "Feedback Trading Strategies: The Case of Greece and Cyprus," South East European Journal of Economics and Business, Sciendo, vol. 13(1), pages 93-99, June.
    19. Diamandis, Panayiotis F., 2008. "Financial liberalization and changes in the dynamic behaviour of emerging market volatility: Evidence from four Latin American equity markets," Research in International Business and Finance, Elsevier, vol. 22(3), pages 362-377, September.
    20. Sumeet Kumar & Binxuan Huang & Ramon Alfonso Villa Cox & Kathleen M. Carley, 2021. "An anatomical comparison of fake-news and trusted-news sharing pattern on Twitter," Computational and Mathematical Organization Theory, Springer, vol. 27(2), pages 109-133, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922009857. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.