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Topological recognition of critical transitions in time series of cryptocurrencies

Author

Listed:
  • Marian Gidea
  • Daniel Goldsmith
  • Yuri Katz
  • Pablo Roldan
  • Yonah Shmalo

Abstract

We analyze the time series of four major cryptocurrencies (Bitcoin, Ethereum, Litecoin, and Ripple) before the digital market crash at the end of 2017 - beginning 2018. We introduce a methodology that combines topological data analysis with a machine learning technique -- $k$-means clustering -- in order to automatically recognize the emerging chaotic regime in a complex system approaching a critical transition. We first test our methodology on the complex system dynamics of a Lorenz-type attractor, and then we apply it to the four major cryptocurrencies. We find early warning signals for critical transitions in the cryptocurrency markets, even though the relevant time series exhibit a highly erratic behavior.

Suggested Citation

  • Marian Gidea & Daniel Goldsmith & Yuri Katz & Pablo Roldan & Yonah Shmalo, 2018. "Topological recognition of critical transitions in time series of cryptocurrencies," Papers 1809.00695, arXiv.org.
  • Handle: RePEc:arx:papers:1809.00695
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    File URL: http://arxiv.org/pdf/1809.00695
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    References listed on IDEAS

    as
    1. Stanis{l}aw Dro.zd.z & Robert Gk{e}barowski & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marcin Wk{a}torek, 2018. "Bitcoin market route to maturity? Evidence from return fluctuations, temporal correlations and multiscaling effects," Papers 1804.05916, arXiv.org, revised Jul 2018.
    2. Hajo Holzmann & Sebastian Vollmer, 2008. "A likelihood ratio test for bimodality in two-component mixtures with application to regional income distribution in the EU," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 57-69, February.
    3. Leopoldo Catania & Stefano Grassi & Francesco Ravazzolo, 2018. "Forecasting Cryptocurrencies Financial Time Series," Working Papers No 5/2018, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    4. J-C Gerlach & Guilherme Demos & Didier Sornette, 2018. "Dissection of Bitcoin's Multiscale Bubble History," Swiss Finance Institute Research Paper Series 18-30, Swiss Finance Institute.
    5. Giacomo Livan & Jun-ichi Inoue & Enrico Scalas, 2012. "On the non-stationarity of financial time series: impact on optimal portfolio selection," Papers 1205.0877, arXiv.org, revised Jul 2012.
    6. Jan-Christian Gerlach & Guilherme Demos & Didier Sornette, 2018. "Dissection of Bitcoin's Multiscale Bubble History from January 2012 to February 2018," Papers 1804.06261, arXiv.org, revised May 2019.
    7. Michael C. Munnix & Takashi Shimada & Rudi Schafer & Francois Leyvraz Thomas H. Seligman & Thomas Guhr & H. E. Stanley, 2012. "Identifying States of a Financial Market," Papers 1202.1623, arXiv.org.
    8. repec:gam:jjrfmx:v:10:y:2017:i:2:p:12-:d:100126 is not listed on IDEAS
    9. Jonathan Chiu & Thorsten V. Koeppl, 2017. "The Economics Of Cryptocurrencies - Bitcoin And Beyond," Working Paper 1389, Economics Department, Queen's University.
    10. repec:gam:jjrfmx:v:10:y:2017:i:4:p:17-:d:113895 is not listed on IDEAS
    11. Leopoldo Catania & Stefano Grassi, 2017. "Modelling Crypto-Currencies Financial Time-Series," CEIS Research Paper 417, Tor Vergata University, CEIS, revised 11 Dec 2017.
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    Cited by:

    1. Pawel Dlotko & Simon Rudkin, 2019. "The Topology of Time Series: Improving Recession Forecasting from Yield Spreads," Working Papers 2019-02, Swansea University, School of Management.

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