With topological data analysis, predicting stock market crashes

We are investigating the evolution of four big US stock market indexes' regular returns after 2000 technology crash and 2007-2009 financial crisis. Our approach is based on topological data processing (TDA). To identify measure phenomena occurring in multidimensional time series, we use persistence homology. obtain time-dependent point cloud sets using a sliding window, which connect space for. research indicates that new method econometric analysis offered by TDA, complements traditional statistical tests. The tool may be used to predict early warning signs declines inevitable.