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Multifractal analysis of financial markets

Author

Listed:
  • Zhi-Qiang Jiang

    (ECUST)

  • Wen-Jie Xie

    (ECUST)

  • Wei-Xing Zhou

    (ECUST)

  • Didier Sornette

    (ETH Zurich)

Abstract

Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis.

Suggested Citation

  • Zhi-Qiang Jiang & Wen-Jie Xie & Wei-Xing Zhou & Didier Sornette, 2018. "Multifractal analysis of financial markets," Papers 1805.04750, arXiv.org.
    • Handle: RePEc:arx:papers:1805.04750
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    Cited by:

    1. Robert Gk{e}barowski & Pawe{l} O'swik{e}cimka & Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z, 2019. "Detecting correlations and triangular arbitrage opportunities in the Forex by means of multifractal detrended cross-correlations analysis," Papers 1906.07491, arXiv.org, revised Oct 2019.
    2. Kristjanpoller, Werner & Bouri, Elie & Takaishi, Tetsuya, 2020. "Cryptocurrencies and equity funds: Evidence from an asymmetric multifractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    3. Zhai, Lu-Sheng & Liu, Ruo-Yu, 2019. "Local detrended cross-correlation analysis for non-stationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 222-233.
    4. Kristjanpoller, Werner & Bouri, Elie, 2019. "Asymmetric multifractal cross-correlations between the main world currencies and the main cryptocurrencies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1057-1071.
    5. Ghosh, Dipak & Chakraborty, Sayantan & Samanta, Shukla, 2019. "Study of translational effect in Tagore’s Gitanjali using Chaos based Multifractal analysis technique," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1343-1354.
    6. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Pawe{l} O'swic{e}cimka & Marek Stanuszek, 2018. "Multifractal cross-correlations between the World Oil and other Financial Markets in 2012-2017," Papers 1812.08548, arXiv.org, revised Jun 2019.
    7. Stanisław Drożdż & Ludovico Minati & Paweł Oświȩcimka & Marek Stanuszek & Marcin Wa̧torek, 2019. "Signatures of the Crypto-Currency Market Decoupling from the Forex," Future Internet, MDPI, vol. 11(7), pages 1-18, July.
    8. Yang, Yan-Hong & Shao, Ying-Hui & Shao, Hao-Lin & Stanley, H. Eugene, 2019. "Revisiting the weak-form efficiency of the EUR/CHF exchange rate market: Evidence from episodes of different Swiss franc regimes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 734-746.
    9. Kristjanpoller, Werner & Minutolo, Marcel C., 2021. "Asymmetric multi-fractal cross-correlations of the price of electricity in the US with crude oil and the natural gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    10. Zhang, Wei & Wang, Pengfei & Li, Xiao & Shen, Dehua, 2018. "The inefficiency of cryptocurrency and its cross-correlation with Dow Jones Industrial Average," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 658-670.
    11. Dai, Peng-Fei & Xiong, Xiong & Zhou, Wei-Xing, 2019. "Visibility graph analysis of economy policy uncertainty indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    12. Zhai, Lusheng & Wu, Yinglin & Yang, Jie & Xie, Hailin, 2020. "Characterizing initiation of gas–liquid churn flows using coupling analysis of multivariate time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    13. Ardalankia, Jamshid & Osoolian, Mohammad & Haven, Emmanuel & Jafari, G. Reza, 2020. "Scaling features of price–volume cross correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    14. Kukacka, Jiri & Kristoufek, Ladislav, 2020. "Do ‘complex’ financial models really lead to complex dynamics? Agent-based models and multifractality," Journal of Economic Dynamics and Control, Elsevier, vol. 113(C).
    15. Yingxiu Zhao & Wei Zhang & Xiangyu Kong, 2019. "Dynamic Cross-Correlations between Participants’ Attentions to P2P Lending and Offline Loan in the Private Lending Market," Complexity, Hindawi, vol. 2019, pages 1-8, December.
    16. Ji, Qiangbiao & Zhang, Xin & Zhu, Yingming, 2020. "Multifractal analysis of the impact of US–China trade friction on US and China soy futures markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    17. Tan, Zhengxun & Liu, Juan & Chen, Juanjuan, 2021. "Detecting stock market turning points using wavelet leaders method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).

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