| CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY |
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Direct Evidence for Inversion Formula in Multifractal Financial Volatility Measure |
| JIANG Zhi-Qiang1,2,3, ZHOU Wei-Xing 1,2,3,4,5 |
| 1School of Business, East China University of Science and Technology, Shanghai 2002372School of Science, East China University of Science and Technology, Shanghai 2002373Research Center for Econophysics, East China University of Science and Technology, Shanghai 2002374Engineering Research Center of Process Systems Engineering (Ministry of Education), East China University of Science and Technology, Shanghai 2002375Research Center on Fictitious Economics and Data Science, Chinese Academy of Sciences, Beijing 100190 |
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| Cite this article: |
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JIANG Zhi-Qiang, ZHOU Wei-Xing 2009 Chin. Phys. Lett. 26 028901 |
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Abstract The inversion formula for conservative multifractal measures was unveiled mathematically a decade ago, which is however not well tested in real complex systems. We propose to verify the inversion formula using high-frequency turbulent financial data. We construct conservative volatility measure based on minutely S&P 500 index from 1982 to 1999 and its inverse measure of exit time. Both the direct and inverse measures exhibit nice multifractal nature, whose scaling ranges are not irrelevant. Empirical investigation shows that the inversion formula holds in financial markets.
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| Keywords:
89.75.Da
89.65.Gh
05.45.Df
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Received: 08 July 2008
Published: 20 January 2009
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| PACS: |
89.75.Da
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(Systems obeying scaling laws)
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89.65.Gh
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(Economics; econophysics, financial markets, business and management)
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05.45.Df
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(Fractals)
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