Mild explocivity, persistent homology and cryptocurrencies' bubbles: An empirical exercise

An empirical investigation was held regarding whether topological properties associated with point clouds formed by cryptocurrencies' prices could contain information on (locally) explosive dynamics of the processes involved. Those dynamics are associated with financial bubbles. The Phillips, Shi and Yu [33,34] (PSY) timestamping method as well as notions associated with the Topological Data Analysis (TDA) like persistent simplicial homology and landscapes were employed on a dataset consisting of the time series of daily closing prices of the Bitcoin, Ethereum, Ripple and Litecoin. The note provides some empirical evidence that TDA could be useful in detecting and timestamping financial bubbles. If robust, such an empirical conclusion opens some interesting paths of further research.