Empirical study of financial crises based on topological data analysis

We analyze financial time series based on topological data analysis to obtain the critical information around 2008 global financial crisis and 2010 European debt crisis. We build an early warning system to detect the critical dates on the financial time series. By constructing complexes on the point clouds data with sliding windows, we explore their topological changes from window to window. The persistence barcodes, diagrams and landscapes are obtained from the complexes of several US’s stock indices. We detect the early warning signal of the 2008 crisis in the first half of 2007. The changes of complexes are also shown in detail. And then we choose several European countries’ typical indices to do a similar work. The topological structures of the complexes change sharply in 2008 and 2010. It shows us clearly that 2008 and 2010 financial crises affected European stock markets greatly. To study the condition of China’s stock markets during the crises, we choose two major stock indices to construct complexes and analyze their changes. The early warning signal is also detected in the early 2007, and China’s stock markets experienced quite a long period of intense turbulence around 2008. However, it was not so serious as US’s and European markets. Furthermore, we also see that European debt crisis did not obviously affect China’s stock markets.