Topological Recognition of Critical Transitions in Time Series of Cryptocurrencies

We analyze four major cryptocurrencies (Bitcoin, Ethereum, Litecoin, and Ripple) before the digital asset market crash at the beginning of 2018. We also analyze Bitcoin before some of the mini-crashes that occurred during the period 2016 - 2018. All relevant time series exhibited a highly erratic behavior.We introduce a methodology that combines topological data analysis with a machine learning technique - k-means clustering - in order to characterize 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. Then we apply it to the four major cryptocurrencies. We find early warning signals for critical transitions, i.e., crashes, in the cryptocurrency markets