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