Topological Time Series Analysis of Market Crashes: A Persistence Homology Approach

In this essay we use a computational topology-based approach on data analysis to study the topological signal by the financial system prior to the onset of a financial collapse. We find that before the onset of one financial collapse, the duration of the 1-dimensional topological features becomes longer, corresponding to a rapid growth in the number of norms in the persistence landscape. Such approach can be applied not only to financial systems but also to the detection of criticality transition in other dynamical systems. We also put features at topological signals into machine learning algorithms to train the models for predicting financial collapses. Comparing with traditional time series methods as well as other training models, our model performs more consistently as well as accurately in providing predictions when applied to new financial time-series data out of the training set.