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

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  • 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
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    References listed on IDEAS

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    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. Bildirici, Melike E. & Sonustun, Bahri, 2021. "Chaotic behavior in gold, silver, copper and bitcoin prices," Resources Policy, Elsevier, vol. 74(C).
    4. 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.
    5. Anna D. Broido & Aaron Clauset, 2019. "Scale-free networks are rare," Nature Communications, Nature, vol. 10(1), pages 1-10, December.
    6. 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.
    7. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    8. 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.
    9. 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).
    10. 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.
    11. Remy Chicheportiche & Jean-Philippe Bouchaud, 2011. "Goodness-of-Fit tests with Dependent Observations," Papers 1106.3016, arXiv.org, revised Aug 2011.
    12. Lahmiri, Salim & Bekiros, Stelios, 2018. "Chaos, randomness and multi-fractality in Bitcoin market," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 28-34.
    13. 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).
    14. Warren E. Weber, 2016. "A Bitcoin Standard: Lessons from the Gold Standard," Staff Working Papers 16-14, Bank of Canada.
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    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).

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