Topological Data Analysis for Identifying Critical Transitions in Cryptocurrency Time Series

In this study, we investigate financial crashes in the cryptocurrency market including both mini and major crashes for two cryptocurrencies, Bitcoin and Ethereum, during the period that the digital market crashed in 2018. By applying techniques in topological data analysis, we are able to predict financial transitions and explore optimal values of the window size and the dimension of point cloud data to obtain good early warning signals. Our results demonstrate good early warning signals before the financial crashes and also show that the L
¹
-norm and C
¹
– norm of persistent landscapes peak before the crashes occur.