Topological recognition of critical transitions in time series of\n cryptocurrencies

Abstract

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