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Topological recognition of critical transitions in time series of cryptocurrencies


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


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.

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  • Marian Gidea & Daniel Goldsmith & Yuri Katz & Pablo Roldan & Yonah Shmalo, 2018. "Topological recognition of critical transitions in time series of cryptocurrencies," Papers 1809.00695,
  • Handle: RePEc:arx:papers:1809.00695

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    References listed on IDEAS

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    Cited by:

    1. Rodrigo Rivera-Castro & Polina Pilyugina & Evgeny Burnaev, 2020. "Topological Data Analysis for Portfolio Management of Cryptocurrencies," Papers 2009.03362,
    2. Eduard Baitinger & Samuel Flegel, 2021. "The better turbulence index? Forecasting adverse financial markets regimes with persistent homology," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 35(3), pages 277-308, September.
    3. Yitao Li & Umar Islambekov & Cuneyt Akcora & Ekaterina Smirnova & Yulia R. Gel & Murat Kantarcioglu, 2019. "Dissecting Ethereum Blockchain Analytics: What We Learn from Topology and Geometry of Ethereum Graph," Papers 1912.10105,
    4. 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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