IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1809.08403.html
   My bibliography  Save this paper

Chaos and Order in the Bitcoin Market

Author

Listed:
  • Josselin Garnier
  • Knut Solna

Abstract

The bitcoin price has surged in recent years and it has also exhibited phases of rapid decay. In this paper we address the question to what extent this novel cryptocurrency market can be viewed as a classic or semi-efficient market. Novel and robust tools for estimation of multi-fractal properties are used to show that the bitcoin price exhibits a very interesting multi-scale correlation structure. This structure can be described by a power-law behavior of the variances of the returns as functions of time increments and it can be characterized by two parameters, the volatility and the Hurst exponent. These power-law parameters, however, vary in time. A new notion of generalized Hurst exponent is introduced which allows us to check if the multi-fractal character of the underlying signal is well captured. It is moreover shown how the monitoring of the power-law parameters can be used to identify regime shifts for the bitcoin price. A novel technique for identifying the regimes switches based on a goodness of fit of the local power-law parameters is presented. It automatically detects dates associated with some known events in the bitcoin market place. A very surprising result is moreover that, despite the wild ride of the bitcoin price in recent years and its multi-fractal and non-stationary character, this price has both local power-law behaviors and a very orderly correlation structure when it is observed on its entire period of existence.

Suggested Citation

  • Josselin Garnier & Knut Solna, 2018. "Chaos and Order in the Bitcoin Market," Papers 1809.08403, arXiv.org, revised Apr 2019.
    • Handle: RePEc:arx:papers:1809.08403
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1809.08403
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
    2. Erhan Bayraktar & H. Vincent Poor & K. Ronnie Sircar, 2004. "Estimating The Fractal Dimension Of The S&P 500 Index Using Wavelet Analysis," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(05), pages 615-643.
    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. Eom, Cheoljun & Choi, Sunghoon & Oh, Gabjin & Jung, Woo-Sung, 2008. "Hurst exponent and prediction based on weak-form efficient market hypothesis of stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(18), pages 4630-4636.
    5. Jiang, Zhi-Qiang & Xie, Wen-Jie & Zhou, Wei-Xing, 2014. "Testing the weak-form efficiency of the WTI crude oil futures market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 235-244.
    6. John Elder & Apostolos Serletis, 2008. "Long memory in energy futures prices," Review of Financial Economics, John Wiley & Sons, vol. 17(2), pages 146-155.
    7. Alvarez-Ramirez, Jose & Cisneros, Myriam & Ibarra-Valdez, Carlos & Soriano, Angel, 2002. "Multifractal Hurst analysis of crude oil prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(3), pages 651-670.
    8. Cajueiro, Daniel O & Tabak, Benjamin M, 2004. "The Hurst exponent over time: testing the assertion that emerging markets are becoming more efficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 521-537.
    9. Alvarez-Ramirez, J. & Rodriguez, E. & Ibarra-Valdez, C., 2018. "Long-range correlations and asymmetry in the Bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 948-955.
    10. Kalamaras, N. & Philippopoulos, K. & Deligiorgi, D. & Tzanis, C.G. & Karvounis, G., 2017. "Multifractal scaling properties of daily air temperature time series," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 38-43.
    11. Laib, Mohamed & Golay, Jean & Telesca, Luciano & Kanevski, Mikhail, 2018. "Multifractal analysis of the time series of daily means of wind speed in complex regions," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 118-127.
    12. 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.
    13. Josselin Garnier & Knut Solna, 2018. "Emergence of Turbulent Epochs in Oil Prices," Papers 1808.09382, arXiv.org, revised Apr 2019.
    14. Gajardo, Gabriel & Kristjanpoller, Werner, 2017. "Asymmetric multifractal cross-correlations and time varying features between Latin-American stock market indices and crude oil market," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 121-128.
    15. Lahmiri, Salim & Bekiros, Stelios, 2018. "Chaos, randomness and multi-fractality in Bitcoin market," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 28-34.
    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. Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Pawe{l} O'swik{e}cimka & Tomasz Stanisz & Marcin Wk{a}torek, 2020. "Complexity in economic and social systems: cryptocurrency market at around COVID-19," Papers 2009.10030, arXiv.org.
    2. Derick Quintino & Jessica Campoli & Heloisa Burnquist & Paulo Ferreira, 2020. "Efficiency of the Brazilian Bitcoin: A DFA Approach," IJFS, MDPI, vol. 8(2), pages 1-9, April.
    3. Omane-Adjepong, Maurice & Alagidede, Imhotep Paul, 2020. "High- and low-level chaos in the time and frequency market returns of leading cryptocurrencies and emerging assets," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.
    5. Bildirici, Melike E. & Sonustun, Bahri, 2021. "Chaotic behavior in gold, silver, copper and bitcoin prices," Resources Policy, Elsevier, vol. 74(C).
    6. 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.

    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. 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.
    2. Garnier, Josselin & Solna, Knut, 2019. "Emergence of turbulent epochs in oil prices," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 281-292.
    3. Josselin Garnier & Knut Solna, 2018. "Emergence of Turbulent Epochs in Oil Prices," Papers 1808.09382, arXiv.org, revised Apr 2019.
    4. 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.
    5. Lee, Min-Jae & Choi, Sun-Yong, 2024. "Insights into the dynamics of market efficiency spillover of financial assets in different equity markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 641(C).
    6. Alvarez-Ramirez, Jose & Alvarez, Jesus & Rodriguez, Eduardo, 2008. "Short-term predictability of crude oil markets: A detrended fluctuation analysis approach," Energy Economics, Elsevier, vol. 30(5), pages 2645-2656, September.
    7. Telli, Şahin & Chen, Hongzhuan & Zhao, Xufeng, 2022. "Detecting multifractality and exposing distributions of local fluctuations: Detrended fluctuation analysis with descriptive statistics pooling," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    8. Jiang, Zhi-Qiang & Xie, Wen-Jie & Zhou, Wei-Xing, 2014. "Testing the weak-form efficiency of the WTI crude oil futures market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 235-244.
    9. 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.
    10. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2018. "Nonextensive triplets in cryptocurrency exchanges," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1069-1074.
    11. Kristjanpoller, Werner & Bouri, Elie & Takaishi, Tetsuya, 2020. "Cryptocurrencies and equity funds: Evidence from an asymmetric multifractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    12. Wang, Yudong & Wu, Chongfeng, 2012. "What can we learn from the history of gasoline crack spreads?: Long memory, structural breaks and modeling implications," Economic Modelling, Elsevier, vol. 29(2), pages 349-360.
    13. Zhang, Wei & Wang, Pengfei & Li, Xiao & Shen, Dehua, 2018. "Quantifying the cross-correlations between online searches and Bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 657-672.
    14. Santos, Fábio Sandro dos & Nascimento, Kerolly Kedma Felix do & Jale, Jader da Silva & Stosic, Tatijana & Marinho, Manoel H.N. & Ferreira, Tiago A.E., 2021. "Mixture distribution and multifractal analysis applied to wind speed in the Brazilian Northeast region," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    15. Shao, Wei & Wang, Jian, 2020. "Does the “ice-breaking” of South and North Korea affect the South Korean financial market?," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    16. Nikolaos A. Kyriazis, 2019. "A Survey on Efficiency and Profitable Trading Opportunities in Cryptocurrency Markets," JRFM, MDPI, vol. 12(2), pages 1-17, April.
    17. 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.
    18. 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).
    19. 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.
    20. 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.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:1809.08403. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.