A persistent-homology-based turbulence index & some applications of TDA on financial markets

TL;DR

This paper introduces a new turbulence index based on persistent homology, a key TDA tool, demonstrating its effectiveness in detecting critical transitions in various financial markets and providing insights for investors.

Contribution

It presents a novel turbulence index derived from persistent homology and reviews recent applications of TDA in financial market analysis, including early turbulence detection.

Findings

The index captures critical transitions in financial data.

It successfully detects market crashes like Black Monday and COVID-19.

TDA offers new insights into financial market dynamics.

Abstract

Topological Data Analysis (TDA) is a modern approach to Data Analysis focusing on the topological features of data; it has been widely studied in recent years and used extensively in Biology, Physics, and many other areas. However, financial markets have been studied slightly through TDA. Here we present a quick review of some recent applications of TDA on financial markets, including applications in the early detection of turbulence periods in financial markets and how TDA can help to get new insights while investing. Also, we propose a new turbulence index based on persistent homology -- the fundamental tool for TDA -- that seems to capture critical transitions in financial data; we tested our index with different financial time series (S&P500, Russel 2000, S&P/BMV IPC and Nikkei 225) and crash events (Black Monday crash, dot-com crash, 2007-08 crash and COVID-19 crash). Furthermore, we include an introduction to persistent homology so the reader can understand this paper without knowing TDA.