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

Author

Listed:
  • Miguel A. Ruiz-Ortiz
  • Jos'e Carlos G'omez-Larra~naga
  • Jes'us Rodr'iguez-Viorato

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.

Suggested Citation

  • Miguel A. Ruiz-Ortiz & Jos'e Carlos G'omez-Larra~naga & Jes'us Rodr'iguez-Viorato, 2022. "A persistent-homology-based turbulence index & some applications of TDA on financial markets," Papers 2203.05603, arXiv.org, revised Jul 2023.
    • Handle: RePEc:arx:papers:2203.05603
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    References listed on IDEAS

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    1. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    2. Gidea, Marian & Goldsmith, Daniel & Katz, Yuri & Roldan, Pablo & Shmalo, Yonah, 2020. "Topological recognition of critical transitions in time series of cryptocurrencies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
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