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A statistical analysis of log-periodic precursors to financial crashes

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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.

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Bibliographic Info

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

Volume (Year): 1 (2001)
Issue (Month): 3 ()
Pages: 346-360

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Handle: RePEc:taf:quantf:v:1:y:2001:i:3:p:346-360

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Cited by:
  1. 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.
  2. Fry, J. M., 2009. "Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion," MPRA Paper 16027, University Library of Munich, Germany.
  3. 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.
  4. 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.
  5. John FRY, 2010. "Bubbles And Crashes In Finance: A Phase Transition From Random To Deterministic Behaviour In Prices," Journal of Applied Research in Finance Bi-Annually, ASERS Publishing, vol. 0(2), pages 131-137, December.
  6. 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.
  7. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
  8. D. Sornette & Y. Malevergne & J. F. Muzy, 2002. "Volatility fingerprints of large shocks: Endogeneous versus exogeneous," Papers cond-mat/0204626, arXiv.org.
  9. Hans-Christian Graf v. Bothmer, 2003. "Significance of log-periodic signatures in cumulative noise," Papers cond-mat/0302507, arXiv.org, revised May 2003.
  10. Wei-Xing Zhou & Didier Sornette, 2002. "Non-Parametric Analyses of Log-Periodic Precursors to Financial Crashes," Papers cond-mat/0205531, arXiv.org.
  11. 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.
  12. Thomas Lux, 2006. "Applications of Statistical Physics in Finance and Economics," Working Papers wpn06-07, Warwick Business School, Finance Group.
  13. Fry, John, 2013. "Bubbles, shocks and elementary technical trading strategies," MPRA Paper 47052, University Library of Munich, Germany.
  14. Fry, John, 2012. "Exogenous and endogenous crashes as phase transitions in complex financial systems," MPRA Paper 36202, University Library of Munich, Germany.
  15. Fry, J. M., 2009. "Bubbles and contagion in English house prices," MPRA Paper 17687, University Library of Munich, Germany.
  16. 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.
  17. 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.
  18. Fry, J. M., 2010. "Gaussian and non-Gaussian models for financial bubbles via econophysics," MPRA Paper 27307, University Library of Munich, Germany.

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