Topology in Finance

Topological Data Analysis (TDA) is usually used to study point cloud data. There are innovative ways to transform time series into point clouds, such as using time-delay embedding (also known as Takens embedding).

Hence, TDA becomes a suitable tool to study time series such as financial time series.

One of the key techniques in TDA is persistent homology, which is based on mathematical theories from algebraic topology. Leading researchers across the world have applied topological methods to the field of finance.

Topological Methods in Finance

  1. Gidea, Marian, and Yuri Katz. “Topological data analysis of financial time series: Landscapes of crashes.” Physica A: Statistical Mechanics and its Applications 491 (2018): 820-834.
  2. Goel, Anubha, Puneet Pasricha, and Aparna Mehra. “Topological data analysis in investment decisions.” Expert Systems with Applications 147 (2020): 113222.
  3. Guo, Hongfeng, et al. “Empirical study of financial crises based on topological data analysis.” Physica A: Statistical Mechanics and its Applications 558 (2020): 124956.
  4. Ismail, Mohd Sabri, et al. “Predicting next day direction of stock price movement using machine learning methods with persistent homology: Evidence from Kuala Lumpur Stock Exchange.” Applied Soft Computing 93 (2020): 106422.
  5. Ismail, Mohd Sabri, Saiful Izzuan Hussain, and Mohd Salmi Md Noorani. “Detecting early warning signals of major financial crashes in Bitcoin using persistent homology.” IEEE Access 8 (2020): 202042-202057.
  6. Majumdar, Sourav, and Arnab Kumar Laha. “Clustering and classification of time series using topological data analysis with applications to finance.” Expert Systems with Applications 162 (2020): 113868.
  7. Baitinger, Eduard, and Samuel Flegel. “The better turbulence index? Forecasting adverse financial markets regimes with persistent homology.” Financial Markets and Portfolio Management 35.3 (2021): 277-308.
  8. Dłotko, P., Wanling Qiu, and S. T. Rudkin. “Financial ratios and stock returns reappraised through a topological data analysis lens.” The European Journal of Finance (2021): 1-25.
  9. Katz, Yuri A., and Alain Biem. “Time-resolved topological data analysis of market instabilities.” Physica A: Statistical Mechanics and its Applications 571 (2021): 125816.
  10. Kim, Wonse, et al. “Investigation of flash crash via topological data analysis.” Topology and its Applications 301 (2021): 107523.
  11. Yen, Peter Tsung-Wen, Kelin Xia, and Siew Ann Cheong. “Understanding Changes in the Topology and Geometry of Financial Market Correlations during a Market Crash.” Entropy 23.9 (2021): 1211.
  12. Yen, Peter Tsung-Wen, and Siew Ann Cheong. “Using topological data analysis (TDA) and persistent homology to analyze the stock markets in Singapore and Taiwan.” Frontiers in Physics (2021): 20.
  13. Ismail, Mohd Sabri, et al. “Early warning signals of financial crises using persistent homology.” Physica A: Statistical Mechanics and its Applications 586 (2022): 126459.