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Measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis

  • Yuan, Ying
  • Zhuang, Xin-tian
  • Jin, Xiu
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    Analyzing the Shanghai stock price index daily returns using MF-DFA method, it is found that there are two different types of sources for multifractality in time series, namely, fat-tailed probability distributions and non-linear temporal correlations. Based on that, a sliding window of 240 frequency data in 5 trading days was used to study stock price index fluctuation. It is found that when the stock price index fluctuates sharply, a strong variability is clearly characterized by the generalized Hurst exponents h(q). Therefore, two measures, Δh and σ, based on generalized Hurst exponents were proposed to compare financial risks before and after Price Limits and Reform of Non-tradable Shares. The empirical results verify the validity of the measures, and this has led to a better understanding of complex stock markets.

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    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 388 (2009)
    Issue (Month): 11 ()
    Pages: 2189-2197

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    Handle: RePEc:eee:phsmap:v:388:y:2009:i:11:p:2189-2197
    Contact details of provider: Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

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    1. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
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    3. Sun, Xia & Chen, Huiping & Yuan, Yongzhuang & Wu, Ziqin, 2001. "Predictability of multifractal analysis of Hang Seng stock index in Hong Kong," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 473-482.
    4. Telesca, Luciano & Lapenna, Vincenzo & Macchiato, Maria, 2005. "Multifractal fluctuations in seismic interspike series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 629-640.
    5. Zhuang, Xin-tian & Huang, Xiao-yuan & Sha, Yan-li, 2004. "Research on the fractal structure in the Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 293-305.
    6. Yuan, Ying & Zhuang, Xin-tian, 2008. "Multifractal description of stock price index fluctuation using a quadratic function fitting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 511-518.
    7. Norouzzadeh, P. & Jafari, G.R., 2005. "Application of multifractal measures to Tehran price index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(2), pages 609-627.
    8. Norouzzadeh, P. & Rahmani, B., 2006. "A multifractal detrended fluctuation description of Iranian rial–US dollar exchange rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 328-336.
    9. Skjeltorp, Johannes A, 2000. "Scaling in the Norwegian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(3), pages 486-528.
    10. Wei, Yu & Wang, Peng, 2008. "Forecasting volatility of SSEC in Chinese stock market using multifractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(7), pages 1585-1592.
    11. Chen, Huiping & Sun, Xia & Wu, Ziqin & Wang, Binghong, 2004. "Enlightenment from various conditional probabilities about Hang Seng index in Hong Kong stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 183-196.
    12. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
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