The better turbulence index? Forecasting adverse financial markets regimes with persistent homology

Persistent homology is the workhorse of modern topological data analysis, which in recent years becomes increasingly powerful due to methodological and computing power advances. In this paper, after equipping the reader with the relevant background on persistent homology, we show how this tool can be harnessed for investment purposes. Specifically, we propose a persistent homology-based turbulence index for the detection of adverse market regimes. With the help of an out-of-sample study, we demonstrate that investment strategies relying on a persistent homology-based turbulence detection outperform investment strategies based on other popular turbulence indices. Additionally, we conduct a stability analysis of our findings. This analysis confirms the results from the previous out-of-sample study, as the outperformance prevails for most configurations of the respective investment strategy and thereby mitigating possible data mining concerns.