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A Bayesian analysis of log-periodic precursors to financial crashes

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Author Info

  • 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.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

Volume (Year): 6 (2006)
Issue (Month): 1 ()
Pages: 15-36

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Handle: RePEc:taf:quantf:v:6:y:2006:i:1:p:15-36

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Related research

Keywords: Financial crashes; Bayesian inference; Log-periodicity;

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Citations

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Cited by:
  1. 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.
  2. Fantazzini, Dean & Geraskin, Petr, 2011. "Everything You Always Wanted to Know about Log Periodic Power Laws for Bubble Modelling but Were Afraid to Ask," MPRA Paper 47869, University Library of Munich, Germany.
  3. Pier Paolo Peirano & Damien Challet, 2012. "Baldovin-Stella stochastic volatility process and Wiener process mixtures," Post-Print hal-00734355, HAL.
  4. Fry, John, 2012. "Exogenous and endogenous crashes as phase transitions in complex financial systems," MPRA Paper 36202, University Library of Munich, Germany.
  5. Fry, J. M., 2009. "Bubbles and contagion in English house prices," MPRA Paper 17687, University Library of Munich, Germany.
  6. 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.
  7. 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.
  8. 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.
  9. L. Lin & Ren R. E & D. Sornette, 2009. "A Consistent Model of `Explosive' Financial Bubbles With Mean-Reversing Residuals," Papers 0905.0128, arXiv.org.
  10. 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.
  11. L. Lin & Ren R.E. & D. Sornette, . "A Consistent Model of `Explosive' Financial Bubbles With Mean-Reversing Residuals," Working Papers CCSS-09-002, ETH Zurich, Chair of Systems Design.
  12. Fry, J. M., 2010. "Gaussian and non-Gaussian models for financial bubbles via econophysics," MPRA Paper 27307, University Library of Munich, Germany.
  13. Fry, John, 2013. "Bubbles, shocks and elementary technical trading strategies," MPRA Paper 47052, University Library of Munich, Germany.
  14. Thomas Lux, 2006. "Applications of Statistical Physics in Finance and Economics," Working Papers wpn06-07, Warwick Business School, Finance Group.

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