  Norms of Persistent Homology introduced in topological data analysis are seen
as indicators of system instability, analogous to the changing predictability
that is captured in financial market uncertainty indexes. This paper
demonstrates norms from the financial markets are significant in explaining
financial uncertainty, whilst macroeconomic uncertainty is only explainable by
market volatility. Meanwhile, volatility is insignificant in the determination
of norms when uncertainty enters the regression. Persistence norms therefore
have potential as a further tool in asset pricing, and also as a means of
capturing signals from financial time series beyond volatility.
