IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v106y2018icp28-34.html
   My bibliography  Save this article

Chaos, randomness and multi-fractality in Bitcoin market

Author

Listed:
  • Lahmiri, Salim
  • Bekiros, Stelios

Abstract

Since its inception, the digital currency market is considerably growing, especially in the most recent years. The main purpose of this paper is to investigate, assess and detect chaos, randomness, and multi-scale temporal correlation structure in prices and returns of this specific virtual and speculative market throughout two distinct time periods; namely under a low-level regime period during which prices slowly increased, and during a high and turbulent regime time period whereby they exponentially increased. We found that chaos is only present in prices during both periods, whilst the level of uncertainty in returns has significantly increased during the high-price time period. Furthermore, both prices and returns exhibit long-range correlations and multi-fractality. The fat-tailed probability distributions are the main source of multi-fractality in the time series of prices and returns. Finally, short (long) fluctuations in returns are dominant during low (high) price-regime time period, respectively. Overall, the high-price regime phase has profoundly revealed consistent nonlinear dynamical patterns in the Bitcoin market.

Suggested Citation

  • Lahmiri, Salim & Bekiros, Stelios, 2018. "Chaos, randomness and multi-fractality in Bitcoin market," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 28-34.
    • Handle: RePEc:eee:chsofr:v:106:y:2018:i:c:p:28-34
    DOI: 10.1016/j.chaos.2017.11.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917304605
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.11.005?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. Zunino, Luciano & Zanin, Massimiliano & Tabak, Benjamin M. & Pérez, Darío G. & Rosso, Osvaldo A., 2009. "Forbidden patterns, permutation entropy and stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2854-2864.
    2. Urquhart, Andrew, 2016. "The inefficiency of Bitcoin," Economics Letters, Elsevier, vol. 148(C), pages 80-82.
    3. 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.
    4. Lahmiri, Salim & Bekiros, Stelios, 2017. "Disturbances and complexity in volatility time series," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 38-42.
    5. Mali, Provash & Mukhopadhyay, Amitabha, 2014. "Multifractal characterization of gold market: A multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 361-372.
    6. Lahmiri, Salim, 2017. "A study on chaos in crude oil markets before and after 2008 international financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 389-395.
    7. Gu, Rongbao & Chen, Hongtao & Wang, Yudong, 2010. "Multifractal analysis on international crude oil markets based on the multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2805-2815.
    8. Lahmiri, Salim, 2015. "Long memory in international financial markets trends and short movements during 2008 financial crisis based on variational mode decomposition and detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 130-138.
    9. Lahmiri, Salim, 2017. "Investigating existence of chaos in short and long term dynamics of Moroccan exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 655-661.
    10. Bigdeli, N. & Afshar, K., 2009. "Chaotic behavior of price in the power markets with pay-as-bid payment mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2560-2569.
    11. Wang, Fang & Liao, Gui-ping & Li, Jian-hui & Li, Xiao-chun & Zhou, Tie-jun, 2013. "Multifractal detrended fluctuation analysis for clustering structures of electricity price periods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5723-5734.
    12. Zunino, Luciano & Fernández Bariviera, Aurelio & Guercio, M. Belén & Martinez, Lisana B. & Rosso, Osvaldo A., 2012. "On the efficiency of sovereign bond markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4342-4349.
    13. Lee, Minhyuk & Song, Jae Wook & Park, Ji Hwan & Chang, Woojin, 2017. "Asymmetric multi-fractality in the U.S. stock indices using index-based model of A-MFDFA," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 28-38.
    14. Cao, Guangxi & Xu, Wei, 2016. "Multifractal features of EUA and CER futures markets by using multifractal detrended fluctuation analysis based on empirical model decomposition," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 212-222.
    15. Çoban, Gürsan & Büyüklü, Ali H., 2009. "Deterministic flow in phase space of exchange rates: Evidence of chaos in filtered series of Turkish Lira–Dollar daily growth rates," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1062-1067.
    16. Cajueiro, Daniel O. & Tabak, Benjamin M., 2009. "Multifractality and herding behavior in the Japanese stock market," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 497-504.
    17. Niu, Hongli & Wang, Jun, 2013. "Complex dynamic behaviors of oriented percolation-based financial time series and Hang Seng index," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 36-44.
    18. Martina, Esteban & Rodriguez, Eduardo & Escarela-Perez, Rafael & Alvarez-Ramirez, Jose, 2011. "Multiscale entropy analysis of crude oil price dynamics," Energy Economics, Elsevier, vol. 33(5), pages 936-947, September.
    19. Lahmiri, Salim, 2017. "On fractality and chaos in Moroccan family business stock returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 29-39.
    20. Chen, Feier & Tian, Kang & Ding, Xiaoxu & Miao, Yuqi & Lu, Chunxia, 2016. "Finite-size effect and the components of multifractality in transport economics volatility based on multifractal detrending moving average method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1058-1066.
    21. Barkoulas, John T., 2008. "Testing for deterministic monetary chaos: Metric and topological diagnostics," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1013-1024.
    22. Olmedo, Elena, 2011. "Is there chaos in the Spanish labour market?," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1045-1053.
    23. BenSaïda, Ahmed & Litimi, Houda, 2013. "High level chaos in the exchange and index markets," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 90-95.
    Full references (including those not matched with items on IDEAS)

    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. Lahmiri, Salim, 2017. "Multifractal analysis of Moroccan family business stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 183-191.
    2. Lahmiri, Salim, 2017. "On fractality and chaos in Moroccan family business stock returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 29-39.
    3. Lahmiri, Salim & Bekiros, Stelios, 2017. "Disturbances and complexity in volatility time series," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 38-42.
    4. Tsionas, Mike G. & Michaelides, Panayotis G., 2017. "Bayesian analysis of chaos: The joint return-volatility dynamical system," MPRA Paper 80632, University Library of Munich, Germany.
    5. Tsionas, Mike G. & Michaelides, Panayotis G., 2017. "Neglected chaos in international stock markets: Bayesian analysis of the joint return–volatility dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 95-107.
    6. Gajardo, Gabriel & Kristjanpoller, Werner D. & Minutolo, Marcel, 2018. "Does Bitcoin exhibit the same asymmetric multifractal cross-correlations with crude oil, gold and DJIA as the Euro, Great British Pound and Yen?," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 195-205.
    7. Takaishi, Tetsuya, 2018. "Statistical properties and multifractality of Bitcoin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 507-519.
    8. 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.
    9. Lahmiri, Salim & Bekiros, Stelios & Salvi, Antonio, 2018. "Long-range memory, distributional variation and randomness of bitcoin volatility," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 43-48.
    10. Aurelio F. Bariviera & Luciano Zunino & Osvaldo A. Rosso, 2018. "An analysis of high-frequency cryptocurrencies prices dynamics using permutation-information-theory quantifiers," Papers 1808.01926, arXiv.org.
    11. Higor Y. D. Sigaki & Matjaz Perc & Haroldo V. Ribeiro, 2019. "Clustering patterns in efficiency and the coming-of-age of the cryptocurrency market," Papers 1901.04967, arXiv.org.
    12. Lahmiri, Salim, 2017. "A study on chaos in crude oil markets before and after 2008 international financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 389-395.
    13. Luiz G. A. Alves & Higor Y. D. Sigaki & Matjaz Perc & Haroldo V. Ribeiro, 2020. "Collective dynamics of stock market efficiency," Papers 2011.14809, arXiv.org.
    14. Lucía Inglada-Pérez & Pablo Coto-Millán, 2021. "A Chaos Analysis of the Dry Bulk Shipping Market," Mathematics, MDPI, vol. 9(17), pages 1-35, August.
    15. Kakinaka, Shinji & Umeno, Ken, 2021. "Exploring asymmetric multifractal cross-correlations of price–volatility and asymmetric volatility dynamics in cryptocurrency markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    16. Lahmiri, Salim & Bekiros, Stelios & Bezzina, Frank, 2020. "Multi-fluctuation nonlinear patterns of European financial markets based on adaptive filtering with application to family business, green, Islamic, common stocks, and comparison with Bitcoin, NASDAQ, ," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    17. Achraf Ghorbel & Wajdi Frikha & Yasmine Snene Manzli, 2022. "Testing for asymmetric non-linear short- and long-run relationships between crypto-currencies and stock markets," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 12(3), pages 387-425, September.
    18. Aggarwal, Divya & Chandrasekaran, Shabana & Annamalai, Balamurugan, 2020. "A complete empirical ensemble mode decomposition and support vector machine-based approach to predict Bitcoin prices," Journal of Behavioral and Experimental Finance, Elsevier, vol. 27(C).
    19. Tetsuya Takaishi, 2017. "Statistical properties and multifractality of Bitcoin," Papers 1707.07618, arXiv.org, revised May 2018.
    20. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2019. "Exploring disorder and complexity in the cryptocurrency space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 548-556.

    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:106:y:2018:i:c:p:28-34. 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.