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Power Law Analysis of Financial Index Dynamics

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  • J. Tenreiro Machado
  • Fernando B. Duarte
  • Gonçalo Monteiro Duarte

Abstract

Power law (PL) and fractional calculus are two faces of phenomena with long memory behavior. This paper applies PL description to analyze different periods of the business cycle. With such purpose the evolution of ten important stock market indices (DAX, Dow Jones, NASDAQ, Nikkei, NYSE, S&P500, SSEC, HSI, TWII, and BSE) over time is studied. An evolutionary algorithm is used for the fitting of the PL parameters. It is observed that the PL curve fitting constitutes a good tool for revealing the signal main characteristics leading to the emergence of the global financial dynamic evolution.

Suggested Citation

  • J. Tenreiro Machado & Fernando B. Duarte & Gonçalo Monteiro Duarte, 2012. "Power Law Analysis of Financial Index Dynamics," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-12, July.
    • Handle: RePEc:hin:jnddns:120518
    DOI: 10.1155/2012/120518
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    References listed on IDEAS

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    1. Carmen Pellicer-Lostao & Ricardo Lopez-Ruiz, 2011. "Transition From Exponential To Power Law Income Distributions In A Chaotic Market," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 21-33.
    2. 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.
    3. Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Stanley, Eugene, 2007. "A unified econophysics explanation for the power-law exponents of stock market activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 81-88.
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