Detecting Early Warning Signals of Major Financial Crashes in Bitcoin Using Persistent Homology

This study explores persistent homology to detect early warning signals of the 2017 and 2019 major financial crashes in Bitcoin. Sliding window is used to obtain point cloud datasets from a multidimensional time series (Bitcoin, Ethereum, Litecoin and Ripple). We apply persistent homology to quantify transient loops that appear in multiscale topological spaces, which associated on each point cloud dataset and encode the quantified information in a persistence landscape. Temporal changes in persistence landscapes are measured via their L
¹
-norms. Consequently, a new representative is attained, called L
¹
-norms time series. The L
¹
-norms is associated with indicators: autocorrelation function at lag 1, variance and mean power spectrum at low frequencies to detect the signals. By using Kendall's tau correlation and significance test, significant rising trend events that occur before major financial crashes in Bitcoin are defined as the signals. A threshold is determined to scan entire data and record all the significant rising trend events. Lastly, we compare L
¹
-norms with residuals time series, which is another representative obtained from de-trending approach. Our result portrays that autocorrelation function at lag 1 and variance of the L
¹
-norms successfully detect early warning signals before the 2017 and 2019 major financial crashes. However, variance of the L
¹
-norms is better since it able to signal another 2018 major financial crash. For the residuals, no early warning signals are detected. Hence, persistent homology provides a better representative than de-trending approach. Overall, persistent homology is a promising method to detect early warning signals of major financial crashes in Bitcoin.