Time-resolved topological data analysis of market instabilities

We apply the novel econometric method, based on the time-resolved topological data analysis, to detect approaching market instabilities in multiple sectors of North American economy. Using the Takens’ embedding and the sliding window’s technique, we detect transient loops that appear in a topological space associated with financial time series and measure their persistence. The latter is encoded in Lp-norms of real-valued functions referred to as “persistence landscapes”. We study the impact of hyperparameters of the method – the size of a rolling window and the dimensionality of the Takens’ embedding – by conducting Monte Carlo simulations with synthetic time series sampled from the Student’s t-distribution with varying degrees of freedom. These numeric experiments reveal that the average value of L1-norm is growing with a rising size of a sliding window and dimensionality of embedding. This finding drives the choice of hyperparameters of the method applied to financial time series. We collect significant evidence that the variance of L1-norm derived from daily log-returns of the sector-level aggregates of credit default swap (CDS) spreads with the sliding window of 50 days and 4D embedding can serve as a leading indicator of an approaching financial crash caused by endogenous market forces and that the equity market lagged the CDS market in this discovery.