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Significance of log-periodic precursors to financial crashes


  • D. Sornette

    (Univ. Nice/CNRS and UCLA)

  • A. Johansen

    (The Niels Bohr Institute)


We clarify the status of log-periodicity associated with speculative bubbles preceding financial crashes. In particular, we address Feigenbaum's [2001] criticism and show how it can be rebuked. Feigenbaum's main result is as follows: ``the hypothesis that the log-periodic component is present in the data cannot be rejected at the 95% confidence level when using all the data prior to the 1987 crash; however, it can be rejected by removing the last year of data.'' (e.g., by removing 15% of the data closest to the critical point). We stress that it is naive to analyze a critical point phenomenon, i.e., a power law divergence, reliably by removing the most important part of the data closest to the critical point. We also present the history of log-periodicity in the present context explaining its essential features and why it may be important. We offer an extension of the rational expectation bubble model for general and arbitrary risk-aversion within the general stochastic discount factor theory. We suggest guidelines for using log-periodicity and explain how to develop and interpret statistical tests of log-periodicity. We discuss the issue of prediction based on our results and the evidence of outliers in the distribution of drawdowns. New statistical tests demonstrate that the 1% to 10% quantile of the largest events of the population of drawdowns of the Nasdaq composite index and of the Dow Jones Industrial Average index belong to a distribution significantly different from the rest of the population. This suggests that very large drawdowns result from an amplification mechanism that may make them more predictable than smaller market moves.

Suggested Citation

  • D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520,
  • Handle: RePEc:arx:papers:cond-mat/0106520

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    References listed on IDEAS

    1. Sornette, D & Malevergne, Y, 2001. "From rational bubbles to crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 40-59.
    2. Adam, M C & Szafarz, A, 1992. "Speculative Bubbles and Financial Markets," Oxford Economic Papers, Oxford University Press, vol. 44(4), pages 626-640, October.
    3. Fabrizio Lillo & Rosario N. Mantegna, 2000. "Symmetry alteration of ensemble return distribution in crash and rally days of financial markets," Papers cond-mat/0002438,
    4. Kirill Ilinski, 1999. "Critical Crashes?," Papers cond-mat/9903142,
    5. Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
    6. J.A. Feigenbaum, 2001. "A statistical analysis of log-periodic precursors to financial crashes-super-," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 346-360, March.
    7. Laurent Laloux & Marc Potters & Rama Cont & Jean-Pierre Aguilar & Jean-Philippe Bouchaud, 1998. "Are financial crashes predictable?," Science & Finance (CFM) working paper archive 9804111, Science & Finance, Capital Fund Management.
    8. A. Johansen & D. Sornette, 1998. "Stock market crashes are outliers," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 1(2), pages 141-143, January.
    9. S. Gluzman & V. I. Yukalov, 1998. "Booms and Crashes in Self-Similar Markets," Papers cond-mat/9810092,
    10. Camerer, Colin, 1989. " Bubbles and Fads in Asset Prices," Journal of Economic Surveys, Wiley Blackwell, vol. 3(1), pages 3-41.
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    12. Woo, Wing Thye, 1987. "Some Evidence of Speculative Bubbles in the Foreign Exchange Markets," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 19(4), pages 499-514, November.
    13. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
    14. A. Johansen & D. Sornette, 1999. "Financial ``Anti-Bubbles'': Log-Periodicity in Gold and Nikkei collapses," Papers cond-mat/9901268,
    15. Sornette, Didier & Johansen, Anders, 1998. "A hierarchical model of financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 581-598.
    16. Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-930, September.
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