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Prediction accuracy and sloppiness of log-periodic functions

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  • David Br'ee
  • Damien Challet
  • Pier Paolo Peirano

Abstract

We show that log-periodic power-law (LPPL) functions are intrinsically very hard to fit to time series. This comes from their sloppiness, the squared residuals depending very much on some combinations of parameters and very little on other ones. The time of singularity that is supposed to give an estimate of the day of the crash belongs to the latter category. We discuss in detail why and how the fitting procedure must take into account the sloppy nature of this kind of model. We then test the reliability of LPPLs on synthetic AR(1) data replicating the Hang Seng 1987 crash and show that even this case is borderline regarding predictability of divergence time. We finally argue that current methods used to estimate a probabilistic time window for the divergence time are likely to be over-optimistic.

Suggested Citation

  • David Br'ee & Damien Challet & Pier Paolo Peirano, 2010. "Prediction accuracy and sloppiness of log-periodic functions," Papers 1006.2010, arXiv.org.
    • Handle: RePEc:arx:papers:1006.2010
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    Cited by:

    1. Min Shu & Ruiqiang Song & Wei Zhu, 2021. "The 'COVID' Crash of the 2020 U.S. Stock Market," Papers 2101.03625, arXiv.org.
    2. Demos, G. & Sornette, D., 2019. "Comparing nested data sets and objectively determining financial bubbles’ inceptions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 661-675.
    3. Papastamatiou, Konstantinos & Karakasidis, Theodoros, 2022. "Bubble detection in Greek Stock Market: A DS-LPPLS model approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    4. Sornette, Didier & Woodard, Ryan & Yan, Wanfeng & Zhou, Wei-Xing, 2013. "Clarifications to questions and criticisms on the Johansen–Ledoit–Sornette financial bubble model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4417-4428.
    5. Grobys, Klaus, 2025. "Is gold in the process of a bubble formation? New evidence from the ex-post global financial crisis period," Research in International Business and Finance, Elsevier, vol. 75(C).
    6. Samuel W. Akingbade & Marian Gidea & Matteo Manzi & Vahid Nateghi, 2023. "Why Topological Data Analysis Detects Financial Bubbles?," Papers 2304.06877, arXiv.org.
    7. 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).
    8. V. Filimonov & G. Demos & D. Sornette, 2017. "Modified profile likelihood inference and interval forecast of the burst of financial bubbles," Quantitative Finance, Taylor & Francis Journals, vol. 17(8), pages 1167-1186, August.
    9. Shu, Min & Song, Ruiqiang & Zhu, Wei, 2021. "The ‘COVID’ crash of the 2020 U.S. Stock market," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    10. Zhou, Wei & Huang, Yang & Chen, Jin, 2018. "The bubble and anti-bubble risk resistance analysis on the metal futures in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 947-957.
    11. Brée, David S. & Joseph, Nathan Lael, 2013. "Testing for financial crashes using the Log Periodic Power Law model," International Review of Financial Analysis, Elsevier, vol. 30(C), pages 287-297.
    12. Guilherme Demos & Didier Sornette, 2017. "Lagrange regularisation approach to compare nested data sets and determine objectively financial bubbles' inceptions," Papers 1707.07162, arXiv.org.
    13. G. Demos & D. Sornette, 2017. "Birth or burst of financial bubbles: which one is easier to diagnose?," Quantitative Finance, Taylor & Francis Journals, vol. 17(5), pages 657-675, May.
    14. Avi Singh & Rajesh Mahadeva & Varun Sarda & Amit Kumar Goyal, 2025. "Quantitative Modeling of Speculative Bubbles, Crash Dynamics, and Critical Transitions in the Stock Market Using the Log-Periodic Power-Law Model," IJFS, MDPI, vol. 13(4), pages 1-18, October.
    15. Riza Demirer & Guilherme Demos & Rangan Gupta & Didier Sornette, 2019. "On the predictability of stock market bubbles: evidence from LPPLS confidence multi-scale indicators," Quantitative Finance, Taylor & Francis Journals, vol. 19(5), pages 843-858, May.
    16. Christopher Lynch & Benjamin Mestel, 2017. "Logistic Model For Stock Market Bubbles And Anti-Bubbles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-24, September.
    17. Fry, John, 2012. "Exogenous and endogenous crashes as phase transitions in complex financial systems," MPRA Paper 36202, University Library of Munich, Germany.
    18. John Fry & McMillan David, 2015. "Stochastic modelling for financial bubbles and policy," Cogent Economics & Finance, Taylor & Francis Journals, vol. 3(1), pages 1002152-100, December.
    19. John Fry, 2014. "Bubbles, shocks and elementary technical trading strategies," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(1), pages 1-13, January.

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