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Scale invariant multiplier and multifractality of absolute returns in stock markets

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  • Zhi-Qiang Jiang

    (ECUST)

  • Wei-Xing Zhou

    (ECUST)

Abstract

The statistical properties of the multipliers of the absolute returns are investigated using one-minute 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 in 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

  • Zhi-Qiang Jiang & Wei-Xing Zhou, 2006. "Scale invariant multiplier and multifractality of absolute returns in stock markets," Papers physics/0609210, arXiv.org, revised Feb 2007.
    • Handle: RePEc:arx:papers:physics/0609210
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    References listed on IDEAS

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    1. 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.
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    1. Rizvi, Syed Aun R. & Dewandaru, Ginanjar & Bacha, Obiyathulla I. & Masih, Mansur, 2014. "An analysis of stock market efficiency: Developed vs Islamic stock markets using MF-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 86-99.
    2. Dewandaru, Ginanjar & Masih, Rumi & Bacha, Obiyathulla Ismath & Masih, A. Mansur. M., 2015. "Developing trading strategies based on fractal finance: An application of MF-DFA in the context of Islamic equities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 223-235.

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