Topological tail dependence: Evidence from forecasting realized volatility

Abstract

This paper proposes a novel theory, coined as Topological Tail Dependence Theory, that links the mathematical theory behind Persistent Homology (PH) and the financial stock market theory. This study also proposes a novel algorithm to measure topological stock market changes as well as the incorporation of these topological changes into forecasting realized volatility (RV) models to improve their forecast performance during turbulent periods. The results of the empirical experimentation of this study provide evidence that the predictions drawn from the Topological Tail Dependence Theory are correct and indicate that the employment of PH information allows nonlinear and neural network models to better forecast RV during a turbulent period.