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Scale invariant distribution and multifractality of volatility multipliers in stock markets

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  • Jiang, Zhi-Qiang
  • Zhou, Wei-Xing

Abstract

The statistical properties of the multipliers of the absolute returns are investigated using 1-min high-frequency data of financial time series. The multiplier distribution is found to be independent of the box size s when s is larger than some crossover scale, providing direct evidence of the existence of scale invariance in financial data. The multipliers with base a=2 are well approximated by a normal distribution and the most probable multiplier scales as a power law with respect to the base a. We unravel that the volatility multipliers possess multifractal nature which is independent of construction of the multipliers, that is, the values of s and a.

Suggested Citation

  • Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2007. "Scale invariant distribution and multifractality of volatility multipliers in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 343-350.
    • Handle: RePEc:eee:phsmap:v:381:y:2007:i:c:p:343-350
    DOI: 10.1016/j.physa.2007.03.015
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    1. Lee, Jae Woo & Eun Lee, Kyoung & Arne Rikvold, Per, 2006. "Multifractal behavior of the Korean stock-market index KOSPI," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 355-361.
    2. Górski, A.Z & Drożdż, S & Speth, J, 2002. "Financial multifractality and its subtleties: an example of DAX," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 496-510.
    3. Baviera, Roberto & Pasquini, Michele & Serva, Maurizio & Vergni, Davide & Vulpiani, Angelo, 2001. "Correlations and multi-affinity in high frequency financial datasets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(3), pages 551-557.
    4. 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.
    5. 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.
    6. A. Z. Gorski & S. Drozdz & J. Speth, 2002. "Financial multifractality and its subtleties: an example of DAX," Papers cond-mat/0205482, arXiv.org.
    7. 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.
    8. Turiel, Antonio & Pérez-Vicente, Conrad J., 2003. "Multifractal geometry in stock market time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 629-649.
    9. Sun, Xia & Chen, Huiping & Wu, Ziqin & Yuan, Yongzhuang, 2001. "Multifractal analysis of Hang Seng index in Hong Kong stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 291(1), pages 553-562.
    10. Kaushik Matia & Yosef Ashkenazy & H. Eugene Stanley, 2003. "Multifractal Properties of Price Fluctuations of Stocks and Commodities," Papers cond-mat/0308012, arXiv.org.
    11. Thomas Lux, 2004. "Detecting Multifractal Properties In Asset Returns: The Failure Of The "Scaling Estimator"," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 481-491.
    12. Muniandy, S.V. & Lim, S.C. & Murugan, R., 2001. "Inhomogeneous scaling behaviors in Malaysian foreign currency exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 407-428.
    13. Bollen, Bernard & Inder, Brett, 2002. "Estimating daily volatility in financial markets utilizing intraday data," Journal of Empirical Finance, Elsevier, vol. 9(5), pages 551-562, December.
    14. Wei, Yu & Huang, Dengshi, 2005. "Multifractal analysis of SSEC in Chinese stock market: A different empirical result from Heng Seng index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 497-508.
    15. Kluiving, René & Pasmanter, Rubén A., 1996. "Stochastic selfsimilar branching and turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 228(1), pages 273-291.
    16. N. Vandewalle & M. Ausloos, 1998. "Sparseness and Roughness of Foreign Exchange Rates," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 9(05), pages 711-719.
    17. Xu, Zhaoxia & Gençay, Ramazan, 2003. "Scaling, self-similarity and multifractality in FX markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 578-590.
    18. Mehmet Balcilar, 2003. "Multifractality of the Istanbul and Moscow Stock Market Returns," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 39(2), pages 5-46, March.
    19. Zhou, Wei-Xing & Yu, Zun-Hong, 2001. "On the properties of random multiplicative measures with the multipliers exponentially distributed," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 294(3), pages 273-282.
    20. Turiel, Antonio & Pérez-Vicente, Conrad J., 2005. "Role of multifractal sources in the analysis of stock market time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 475-496.
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