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Self-Similar Log-Periodic Structures In Western Stock Markets From 2000

Author

Listed:
  • M. BARTOLOZZI

    (Special Research Centre for the Subatomic Structure of Matter (CSSM), University of Adelaide, Adelaide, SA 5005, Australia)

  • S. DROŻDŻ

    (Institute of Nuclear Physics, Radzikowskiego 152, 31–342 Kraków, Poland;
    Institute of Physics, University of Rzeszów, PL-35-310 Rzeszów, Poland)

  • D. B. LEINWEBER

    (Special Research Centre for the Subatomic Structure of Matter (CSSM), University of Adelaide, Adelaide, SA 5005, Australia)

  • J. SPETH

    (Institute für Kernphysik, Forschungszentrum Jülich, D–52425 Jülich, Germany)

  • A. W. THOMAS

    (Special Research Centre for the Subatomic Structure of Matter (CSSM), University of Adelaide, Adelaide, SA 5005, Australia;
    Jefferson Laboratory, 12000 Jefferson Ave., Newport News, VA 23606, USA)

Abstract

The presence of log-periodic structures before and after stock market crashes is considered to be an imprint of an intrinsic discrete scale invariance (DSI) in this complex system. The fractal framework of the theory leaves open the possibility of observing self-similar log-periodic structures at different time scales. In the present work, we analyze the daily closures of four of the most important indices worldwide since 2000: the DAX for Germany and the NASDAQ-100, the S&P 500 and the Dow Jones for the United States. The qualitative behavior of these different markets is similar during the temporal frame studied. Evidence is found for decelerating log-periodic oscillations of duration about two years and starting in September 2000. Moreover, a nested sub-structure starting in May 2002 is revealed, bringing more evidence to support the hypothesis of self-similar, log-periodic behavior. Ongoing log-periodic oscillations are also revealed. A Lomb analysis over the aforementioned periods indicates a preferential scaling factorλ~2. Higher order harmonics are also present. The spectral pattern of the data has been found to be similar to that of a Weierstrass-type function, used as a prototype of a log-periodic fractal function.

Suggested Citation

  • M. Bartolozzi & S. Drożdż & D. B. Leinweber & J. Speth & A. W. Thomas, 2005. "Self-Similar Log-Periodic Structures In Western Stock Markets From 2000," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(09), pages 1347-1361.
    • Handle: RePEc:wsi:ijmpcx:v:16:y:2005:i:09:n:s0129183105007972
    DOI: 10.1142/S0129183105007972
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    Cited by:

    1. Shu, Min & Zhu, Wei, 2020. "Detection of Chinese stock market bubbles with LPPLS confidence indicator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    2. Zhou, Wei & Huang, Yang & Chen, Jin, 2018. "The bubble and anti-bubble risk resistance analysis on the metal futures in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 947-957.

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