Topological Data Analysis of Financial Time Series
We apply persistence homology to detect and quantify topological patterns that appear in multidimensional time series. Using a sliding window, we extract time-dependent point cloud data sets, for which we compute persistence homology. We use persistence landscapes to quantify the temporal changes in the time series. We test this approach on multidimensional time series generated by various non-linear and non-equilibrium models. As an alternative approach, we construct correlation networks, and track changes in the topology of these networks.
We apply this method to detect early signs for financial bubbles in market indices and asset prices. As case studies, we consider the US stock market indices during the technology crash of 2000, and the financial crisis of 2007-2009, as well as at the prices of cryptocurrencies.
This is based on joint work with Yuri Katz (Standard and Poor's Global Market Intelligence), and Pablo Roldan, Daniel Goldsmith, and Yonah Shmalo (Yeshiva University).