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Financial multifractality and its subtleties: an example of DAX

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  • A. Z. Gorski
  • S. Drozdz
  • J. Speth

Abstract

Detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency Deutsche Aktienindex data. The tail index ($\alpha$), the Renyi exponents based on the box counting algorithm for the graph ($d_q$) and the generalized Hurst exponents ($H_q$) are computed in parallel for short and daily return times. The results indicate a more complicated nature of the stock market dynamics than just consistent multifractal.

Suggested Citation

  • A. Z. Gorski & S. Drozdz & J. Speth, 2002. "Financial multifractality and its subtleties: an example of DAX," Papers cond-mat/0205482, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0205482
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    1. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2008. "Multifractal analysis of Chinese stock volatilities based on the partition function approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4881-4888.
    2. Ruan, Yong-Ping & Zhou, Wei-Xing, 2011. "Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1646-1654.
    3. Charutha, S. & Gopal Krishna, M. & Manimaran, P., 2020. "Multifractal analysis of Indian public sector enterprises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    4. Cao, Guangxi & Xu, Wei, 2016. "Nonlinear structure analysis of carbon and energy markets with MFDCCA based on maximum overlap wavelet transform," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 505-523.
    5. Zhou, Wei-Xing, 2012. "Finite-size effect and the components of multifractality in financial volatility," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 147-155.
    6. Leal, Sandrine Jacob & Napoletano, Mauro, 2019. "Market stability vs. market resilience: Regulatory policies experiments in an agent-based model with low- and high-frequency trading," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 15-41.
    7. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2008. "Multifractality in stock indexes: Fact or Fiction?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3605-3614.
    8. Jang, Minchul & Yoon, Soeun & Jung, Seoyoung & Min, Baehyun, 2024. "Simulating and assessing carbon markets: Application to the Korean and the EU ETSs," Renewable and Sustainable Energy Reviews, Elsevier, vol. 195(C).
    9. Ankudinov, Andrei & Ibragimov, Rustam & Lebedev, Oleg, 2017. "Sanctions and the Russian stock market," Research in International Business and Finance, Elsevier, vol. 40(C), pages 150-162.
    10. Lee, Hojin & Chang, Woojin, 2015. "Multifractal regime detecting method for financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 117-129.
    11. Wang, Lei & Liu, Lutao, 2020. "Long-range correlation and predictability of Chinese stock prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    12. Hasan, Rashid & Mohammed Salim, M., 2017. "Power law cross-correlations between price change and volume change of Indian stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 620-631.
    13. Chen, Ting-Ting & Zheng, Bo & Li, Yan & Jiang, Xiong-Fei, 2018. "Information driving force and its application in agent-based modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 593-601.
    14. Schadner, Wolfgang, 2021. "On the persistence of market sentiment: A multifractal fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    15. Laura Raisa Miloş & Cornel Haţiegan & Marius Cristian Miloş & Flavia Mirela Barna & Claudiu Boțoc, 2020. "Multifractal Detrended Fluctuation Analysis (MF-DFA) of Stock Market Indexes. Empirical Evidence from Seven Central and Eastern European Markets," Sustainability, MDPI, vol. 12(2), pages 1-15, January.
    16. Alvarez-Ramírez, José & Rodríguez, Eduardo, 2012. "Temporal variations of serial correlations of trading volume in the US stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(16), pages 4128-4135.
    17. 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.

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