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A statistical analysis of log-periodic precursors to financial crashes-super-

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  • J.A. Feigenbaum

Abstract

Motivated by the hypothesis that financial crashes are macroscopic examples of critical phenomena associated with a discrete scaling symmetry, we reconsider the evidence of log-periodic precursors to financial crashes and test the prediction that log-periodic oscillations in a financial index are embedded in the mean function of this index (conditional upon no crash having yet occurred). In particular, we examine the first differences of the logarithm of the S&P 500 prior to the October 1987 crash and find the log-periodic component of this time series is not statistically significant if we exclude the last year of data before the crash. We also examine the claim that two separate mechanisms are needed to explain the frequency distribution of draw downs in the S&P 500 and find the evidence supporting this claim to be unconvincing.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:quantf:v:1:y:2001:i:3:p:346-360 DOI: 10.1088/1469-7688/1/3/306
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. 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.
    2. Wosnitza, Jan Henrik & Leker, Jens, 2014. "Can log-periodic power law structures arise from random fluctuations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 228-250.
    3. Hans-Christian Graf v. Bothmer, 2003. "Significance of log-periodic signatures in cumulative noise," Papers cond-mat/0302507, arXiv.org, revised May 2003.
    4. Fry, J. M., 2010. "Gaussian and non-Gaussian models for financial bubbles via econophysics," MPRA Paper 27307, University Library of Munich, Germany.
    5. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
    6. 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.
    7. Thomas Lux, 2006. "Applications of Statistical Physics in Finance and Economics," Working Papers wpn06-07, Warwick Business School, Finance Group.
    8. John M. Fry, 2009. "Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion," EERI Research Paper Series EERI_RP_2009_10, Economics and Econometrics Research Institute (EERI), Brussels.
    9. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, pages 132-133.
    10. Thomas Lux, 2009. "Applications of Statistical Physics in Finance and Economics," Chapters,in: Handbook of Research on Complexity, chapter 9 Edward Elgar Publishing.
    11. Lux, Thomas, 2008. "Applications of statistical physics in finance and economics," Kiel Working Papers 1425, Kiel Institute for the World Economy (IfW).
    12. Fry, John, 2012. "Exogenous and endogenous crashes as phase transitions in complex financial systems," MPRA Paper 36202, University Library of Munich, Germany.
    13. 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.
    14. Zhou, Wei-Xing & Sornette, Didier, 2006. "Is there a real-estate bubble in the US?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 297-308.
    15. 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.
    16. D. Sornette & Y. Malevergne & J. F. Muzy, 2002. "Volatility fingerprints of large shocks: Endogeneous versus exogeneous," Papers cond-mat/0204626, arXiv.org.
    17. Vakhtina, Elena & Wosnitza, Jan Henrik, 2015. "Capital market based warning indicators of bank runs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 304-320.
    18. Fry, J. M., 2009. "Bubbles and contagion in English house prices," MPRA Paper 17687, University Library of Munich, Germany.
    19. Wei-Xing Zhou & Didier Sornette, 2002. "Non-Parametric Analyses of Log-Periodic Precursors to Financial Crashes," Papers cond-mat/0205531, arXiv.org.
    20. Wosnitza, Jan Henrik & Leker, Jens, 2014. "Why credit risk markets are predestined for exhibiting log-periodic power law structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 427-449.
    21. Filimonov, V. & Sornette, D., 2013. "A stable and robust calibration scheme of the log-periodic power law model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3698-3707.
    22. Fry, J. M., 2010. "Bubbles and crashes in finance: A phase transition from random to deterministic behaviour in prices," MPRA Paper 24778, University Library of Munich, Germany.
    23. Lin, L. & Ren, R.E. & Sornette, D., 2014. "The volatility-confined LPPL model: A consistent model of ‘explosive’ financial bubbles with mean-reverting residuals," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 210-225.
    24. Wosnitza, Jan Henrik & Denz, Cornelia, 2013. "Liquidity crisis detection: An application of log-periodic power law structures to default prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3666-3681.

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