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Non-Parametric Analyses of Log-Periodic Precursors to Financial Crashes

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  • Wei-Xing Zhou

    (UCLA)

  • Didier Sornette

    (UCLA and CNRS-Univ. Nice)

Abstract

We apply two non-parametric methods to test further the hypothesis that log-periodicity characterizes the detrended price trajectory of large financial indices prior to financial crashes or strong corrections. The analysis using the so-called (H,q)-derivative is applied to seven time series ending with the October 1987 crash, the October 1997 correction and the April 2000 crash of the Dow Jones Industrial Average (DJIA), the Standard & Poor 500 and Nasdaq indices. The Hilbert transform is applied to two detrended price time series in terms of the ln(t_c-t) variable, where t_c is the time of the crash. Taking all results together, we find strong evidence for a universal fundamental log-frequency $f = 1.02 \pm 0.05$ corresponding to the scaling ratio $\lambda = 2.67 \pm 0.12$. These values are in very good agreement with those obtained in past works with different parametric techniques.

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  • Wei-Xing Zhou & Didier Sornette, 2002. "Non-Parametric Analyses of Log-Periodic Precursors to Financial Crashes," Papers cond-mat/0205531, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0205531
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    References listed on IDEAS

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    1. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
    2. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 452-471.
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    5. Anders Johansen & Olivier Ledoit & Didier Sornette, 2000. "Crashes As Critical Points," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 219-255.
    6. 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.
    7. Anders Johansen & Didier Sornette, 1999. "Critical Crashes," Papers cond-mat/9901035, arXiv.org.
    8. Mansilla, R., 2001. "Algorithmic complexity of real financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 483-492.
    9. Wei-Xing Zhou & Didier Sornette, 2002. "Statistical Significance Of Periodicity And Log-Periodicity With Heavy-Tailed Correlated Noise," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 137-169.
    10. A. Johansen & D. Sornette, 1999. "Financial "Anti-Bubbles": Log-Periodicity In Gold And Nikkei Collapses," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 563-575.
    11. R. Mansilla, 2001. "Algorithmic Complexity in Real Financial Markets," Papers cond-mat/0104472, arXiv.org.
    12. A. Johansen & D. Sornette, 1999. "Financial ``Anti-Bubbles'': Log-Periodicity in Gold and Nikkei collapses," Papers cond-mat/9901268, arXiv.org.
    13. D. Sornette & J. V. Andersen, 2002. "A Nonlinear Super-Exponential Rational Model Of Speculative Financial Bubbles," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 171-187.
    14. Tél, Tamás & Vollmer, Jürgen & Mátyás, László, 2003. "Comments on the paper ‘Particles, maps and irreversible thermodynamics’ by E.G.D. Cohen, L. Rondoni, Physica A 306 (2002) 117," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 323-326.
    15. D. Sornette & J. V. Andersen, 2001. "A Nonlinear Super-Exponential Rational Model of Speculative Financial Bubbles," Papers cond-mat/0104341, arXiv.org, revised Apr 2002.
    16. Anders Johansen & Didier Sornette, 2000. "The Nasdaq crash of April 2000: Yet another example of log-periodicity in a speculative bubble ending in a crash," Papers cond-mat/0004263, arXiv.org, revised May 2000.
    17. Anders Johansen & Didier Sornette, 2001. "Bubbles And Anti-Bubbles In Latin-American, Asian And Western Stock Markets: An Empirical Study," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(06), pages 853-920.
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    2. Vandermarliere, B. & Ryckebusch, J. & Schoors, K. & Cauwels, P. & Sornette, D., 2017. "Discrete hierarchy of sizes and performances in the exchange-traded fund universe," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 111-123.
    3. Jiang, Zhi-Qiang & Zhou, Wei-Xing & Sornette, Didier & Woodard, Ryan & Bastiaensen, Ken & Cauwels, Peter, 2010. "Bubble diagnosis and prediction of the 2005-2007 and 2008-2009 Chinese stock market bubbles," Journal of Economic Behavior & Organization, Elsevier, vol. 74(3), pages 149-162, June.
    4. Cheng, Fangzheng & Fan, Tijun & Fan, Dandan & Li, Shanling, 2018. "The prediction of oil price turning points with log-periodic power law and multi-population genetic algorithm," Energy Economics, Elsevier, vol. 72(C), pages 341-355.
    5. 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.
    6. 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.
    7. Sornette, Didier & Zhou, Wei-Xing, 2004. "Evidence of fueling of the 2000 new economy bubble by foreign capital inflow: implications for the future of the US economy and its stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 412-440.
    8. Damian Smug & Peter Ashwin & Didier Sornette, 2018. "Predicting financial market crashes using ghost singularities," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-20, March.
    9. 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.
    10. 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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