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Why Topological Data Analysis Detects Financial Bubbles?

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  • Samuel W. Akingbade
  • Marian Gidea
  • Matteo Manzi
  • Vahid Nateghi

Abstract

We present a heuristic argument for the propensity of Topological Data Analysis (TDA) to detect early warning signals of critical transitions in financial time series. Our argument is based on the Log-Periodic Power Law Singularity (LPPLS) model, which characterizes financial bubbles as super-exponential growth (or decay) of an asset price superimposed with oscillations increasing in frequency and decreasing in amplitude when approaching a critical transition (tipping point). We show that whenever the LPPLS model is fitting with the data, TDA generates early warning signals. As an application, we illustrate this approach on a sample of positive and negative bubbles in the Bitcoin historical price.

Suggested Citation

  • Samuel W. Akingbade & Marian Gidea & Matteo Manzi & Vahid Nateghi, 2023. "Why Topological Data Analysis Detects Financial Bubbles?," Papers 2304.06877, arXiv.org.
    • Handle: RePEc:arx:papers:2304.06877
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    References listed on IDEAS

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    1. Maximilian Seyrich & Didier Sornette, 2016. "Micro-foundation using percolation theory of the finite time singular behavior of the crash hazard rate in a class of rational expectation bubbles," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(10), pages 1-20, October.
    2. Peter C. B. Phillips & Jun Yu, 2011. "Dating the timeline of financial bubbles during the subprime crisis," Quantitative Economics, Econometric Society, vol. 2(3), pages 455-491, November.
    3. Song, Ruiqiang & Shu, Min & Zhu, Wei, 2022. "The 2020 global stock market crash: Endogenous or exogenous?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    4. Shu, Min & Zhu, Wei, 2020. "Detection of Chinese stock market bubbles with LPPLS confidence indicator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    5. Umar Islambekov & Monisha Yuvaraj & Yulia R. Gel, 2020. "Harnessing the power of topological data analysis to detect change points," Environmetrics, John Wiley & Sons, Ltd., vol. 31(1), February.
    6. Akcora, Cuneyt Gurcan & Dixon, Matthew F. & Gel, Yulia R. & Kantarcioglu, Murat, 2018. "Bitcoin risk modeling with blockchain graphs," Economics Letters, Elsevier, vol. 173(C), pages 138-142.
    7. Maximilian Seyrich & Didier Sornette, 2016. "Micro-foundation using percolation theory of the finite-time singular behavior of the crash hazard rate in a class of rational expectation bubbles," Papers 1601.07707, arXiv.org.
    8. Cuneyt Akcora & Matthew Dixon & Yulia Gel & Murat Kantarcioglu, 2018. "Bitcoin Risk Modeling with Blockchain Graphs," Papers 1805.04698, arXiv.org.
    9. Olivier J. Blanchard & Mark W. Watson, 1982. "Bubbles, Rational Expectations and Financial Markets," NBER Working Papers 0945, National Bureau of Economic Research, Inc.
    10. L. Lin & D. Sornette, 2013. "Diagnostics of rational expectation financial bubbles with stochastic mean-reverting termination times," The European Journal of Finance, Taylor & Francis Journals, vol. 19(5), pages 344-365, May.
    11. Hyun-U Sohn & Didier Sornette, 2017. "Bubbles as violations of efficient time-scales," Working Papers Series 65, Institute for New Economic Thinking.
    12. Anders Johansen & Olivier Ledoit & Didier Sornette, 2000. "Crashes As Critical Points," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 219-255.
    13. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
    14. Shu, Min & Zhu, Wei, 2020. "Real-time prediction of Bitcoin bubble crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    15. Simon Rudkin & Wanling Qiu & Pawel Dlotko, 2021. "Uncertainty, volatility and the persistence norms of financial time series," Papers 2110.00098, arXiv.org.
    16. Yan, Wanfeng & Woodard, Ryan & Sornette, Didier, 2012. "Diagnosis and prediction of rebounds in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1361-1380.
    17. Katz, Yuri A. & Biem, Alain, 2021. "Time-resolved topological data analysis of market instabilities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 571(C).
    18. Fry, John & Cheah, Eng-Tuck, 2016. "Negative bubbles and shocks in cryptocurrency markets," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 343-352.
    19. Maximilian Seyrich & Didier Sornette, 2016. "Micro-Foundation Using Percolation Theory of the Finite-Time Singular Behavior of the Crash Hazard Rate in a Class of Rational Expectation Bubbles," Swiss Finance Institute Research Paper Series 16-03, Swiss Finance Institute.
    20. David S. Br�e & Damien Challet & Pier Paolo Peirano, 2013. "Prediction accuracy and sloppiness of log-periodic functions," Quantitative Finance, Taylor & Francis Journals, vol. 13(2), pages 275-280, January.
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