Uncertainty, volatility and the persistence norms of financial time series

Norms of Persistent Homology, introduced in topological data analysis, are indicators of system instability, analogous to the changing predictability that is captured in financial market uncertainty indexes. Differentiating observed and unobserved measures of uncertainty, this paper demonstrates a contemporaneous link between persistence norms and uncertainty of all known types. Extending to a dynamic modelling framework provides evidence that unobserved uncertainty Granger causes persistence norms. Further, study of dynamic correlations between persistence norms, volatility and unobserved uncertainty shows that correlations between unobserved uncertainty and persistence norms increase ahead of market crashes. Evidence from the dynamic analysis of the persistence norm–uncertainty relationship provided herein supports the early conclusion that persistence norms provide a signal of impending market crashes. Persistence norms therefore have potential as a further tool in asset pricing, capturing signals from financial time series beyond volatility. •Topological data analysis signals offer understanding of dynamic financial system.•Volatility and uncertainty cannot span the persistence norms of financial markets.•Persistence norms recover pre-crisis values quicker than volatility heralding recovery.•Dynamic correlations provide motivation for persistence norms as crash warning.•Persistence norms offer additional signal for capturing financial market behaviour.