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A Bayesian analysis of log-periodic precursors to financial crashes

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  • George Chang
  • James Feigenbaum

Abstract

A large number of papers have been written by physicists documenting an alleged signature of imminent financial crashes involving so-called log-periodic oscillations-oscillations which are periodic with respect to the logarithm of the time to the crash. In addition to the obvious practical implications of such a signature, log-periodicity has been taken as evidence that financial markets can be modelled as complex statistical-mechanics systems. However, while many log-periodic precursors have been identified, the statistical significance of these precursors and their predictive power remain controversial in part because log-periodicity is ill-suited for study with classical methods. This paper is the first effort to apply Bayesian methods in the testing of log-periodicity. Specifically, we focus on the Johansen-Ledoit-Sornette (JLS) model of log periodicity. Using data from the S&P 500 prior to the October 1987 stock market crash, we find that, if we do not consider crash probabilities, a null hypothesis model without log-periodicity outperforms the JLS model in terms of marginal likelihood. If we do account for crash probabilities, which has not been done in the previous literature, the JLS model outperforms the null hypothesis, but only if we ignore the information obtained by standard classical methods. If the JLS model is true, then parameter estimates obtained by curve fitting have small posterior probability. Furthermore, the data set contains negligible information about the oscillation parameters, such as the frequency parameter that has received the most attention in the previous literature.

Suggested Citation

  • George Chang & James Feigenbaum, 2006. "A Bayesian analysis of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 15-36.
    • Handle: RePEc:taf:quantf:v:6:y:2006:i:1:p:15-36
    DOI: 10.1080/14697680500511017
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    References listed on IDEAS

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    Cited by:

    1. Fry, J. M., 2010. "Gaussian and non-Gaussian models for financial bubbles via econophysics," MPRA Paper 27307, University Library of Munich, Germany.
    2. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    3. Thomas Lux, 2009. "Applications of Statistical Physics in Finance and Economics," Chapters, in: J. Barkley Rosser Jr. (ed.), Handbook of Research on Complexity, chapter 9, Edward Elgar Publishing.
    4. 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).
    5. Fry, J. M., 2009. "Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion," MPRA Paper 16027, University Library of Munich, Germany.
    6. Kozłowska, M. & Denys, M. & Wiliński, M. & Link, G. & Gubiec, T. & Werner, T.R. & Kutner, R. & Struzik, Z.R., 2016. "Dynamic bifurcations on financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 126-142.
    7. Petr Geraskin & Dean Fantazzini, 2013. "Everything you always wanted to know about log-periodic power laws for bubble modeling but were afraid to ask," The European Journal of Finance, Taylor & Francis Journals, vol. 19(5), pages 366-391, May.
    8. Pawel Dlotko & Simon Rudkin, 2019. "The Topology of Time Series: Improving Recession Forecasting from Yield Spreads," Working Papers 2019-02, Swansea University, School of Management.
    9. Fry, John, 2012. "Exogenous and endogenous crashes as phase transitions in complex financial systems," MPRA Paper 36202, University Library of Munich, Germany.
    10. L. Lin & Ren R. E & D. Sornette, 2009. "A Consistent Model of `Explosive' Financial Bubbles With Mean-Reversing Residuals," Papers 0905.0128, arXiv.org.
    11. 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.
    12. 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.
    13. 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.
    14. P. Peirano & D. Challet, 2012. "Baldovin-Stella stochastic volatility process and Wiener process mixtures," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 85(8), pages 1-12, August.
    15. Lux, Thomas, 2008. "Applications of statistical physics in finance and economics," Kiel Working Papers 1425, Kiel Institute for the World Economy (IfW Kiel).
    16. Fry, J. M., 2009. "Bubbles and contagion in English house prices," MPRA Paper 17687, University Library of Munich, Germany.
    17. 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.
    18. L. Lin & Ren R.E. & D. Sornette, "undated". "A Consistent Model of `Explosive' Financial Bubbles With Mean-Reversing Residuals," Working Papers CCSS-09-002, ETH Zurich, Chair of Systems Design.
    19. 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.
    20. 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.
    21. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    22. 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.

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