Uncertainty, volatility and the persistence norms of financial time series

TL;DR

This paper explores how topological data analysis norms relate to financial market uncertainty and volatility, suggesting they can serve as novel indicators for asset pricing and market stability beyond traditional volatility measures.

Contribution

It demonstrates that persistence norms from topological data analysis significantly explain financial uncertainty, offering a new tool for asset pricing and market analysis.

Findings

Persistence norms are significant in explaining financial uncertainty.

Market volatility explains macroeconomic uncertainty.

Persistence norms are independent of volatility when uncertainty is included.

Abstract

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.