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Nonparametric Analyses Of Log-Periodic Precursors To Financial Crashes

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  • WEI-XING ZHOU

    (Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095, USA)

  • DIDIER SORNETTE

    (Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095, USA;
    Department of Earth and Space Sciences, University of California, Los Angeles, CA 90095, USA;
    Laboratoire de Physique de la Matière Condensée, CNRS UMR 6622 and Université de Nice-Sophia Antipolis, 06108 Nice Cedex 2, France)

Abstract

We apply two nonparametric methods to further test the hypothesis that log-periodicity characterizes the detrended price trajectory of large financial indices prior to financial crashes or strong corrections. The term "parametric" refers here to the use of the log-periodic power law formula to fit the data; in contrast, "nonparametric" refers to the use of general tools such as Fourier transform, and in the present case the Hilbert transform and the so-called(H, q)-analysis. The analysis using the(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 theln(tc-t)variable, wheretcis the time of the crash. Taking all results together, we find strong evidence for a universal fundamental log-frequencyf=1.02±0.05corresponding to the scaling ratioλ=2.67±0.12. These values are in very good agreement with those obtained in earlier works with different parametric techniques. This note is extracted from a long unpublished report with 58 figures available at, which extensively describes the evidence we have accumulated on these seven time series, in particular by presenting all relevant details so that the reader can judge for himself or herself the validity and robustness of the results.

Suggested Citation

  • Wei-Xing Zhou & Didier Sornette, 2003. "Nonparametric Analyses Of Log-Periodic Precursors To Financial Crashes," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(08), pages 1107-1125.
    • Handle: RePEc:wsi:ijmpcx:v:14:y:2003:i:08:n:s0129183103005212
    DOI: 10.1142/S0129183103005212
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    References listed on IDEAS

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    9. 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. 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.
    5. 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.
    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. 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.
    8. 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.
    9. 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.
    10. 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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