Topological Data Analysis of Financial Time Series: Landscapes of Crashes
November 19, 2019
We introduce a new method, based on the topological data analysis (TDA), to financial time series and detect early warning signals of approaching financial crashes. Analyzes of the time-series of daily log-returns of major US stock market indices and cryptocurrencies shows that in the vicinity of financial meltdowns, the Lp-norms of persistence topological landscapes exhibit strong growth. Remarkably, the average spectral density at low frequencies of the derived Lp-norms demonstrates a strong rising trend at least 100 trading days prior to either dotcom crash on 03/10/2000, or to the Lehman bankruptcy on 09/15/2008. Our study suggests that TDA provides a new type of predictive analytics, which complements the standard statistical measures. Our approach is very general and can be used beyond the analysis of financial time series.