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Joint multifractal analysis based on wavelet leaders

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Listed:
  • Zhi-Qiang Jiang

    (ECUST, BU)

  • Yan-Hong Yang

    (ECUST, BU)

  • Gang-Jin Wang

    (HNU, BU)

  • Wei-Xing Zhou

    (ECUST)

Abstract

Mutually interacting components form complex systems and the outputs of these components are usually long-range cross-correlated. Using wavelet leaders, we propose a method of characterizing the joint multifractal nature of these long-range cross correlations, a method we call joint multifractal analysis based on wavelet leaders (MF-X-WL). We test the validity of the MF-X-WL method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. Both experiments indicate that MF-X-WL is capable to detect the cross correlations in synthetic data with acceptable estimating errors. We also apply the MF-X-WL method to the pairs of series from financial markets (returns and volatilities) and online worlds (online numbers of different genders and different societies) and find an intriguing joint multifractal behavior.

Suggested Citation

  • Zhi-Qiang Jiang & Yan-Hong Yang & Gang-Jin Wang & Wei-Xing Zhou, 2016. "Joint multifractal analysis based on wavelet leaders," Papers 1611.00897, arXiv.org.
    • Handle: RePEc:arx:papers:1611.00897
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    Cited by:

    1. Ruan, Qingsong & Zhang, Manqian & Lv, Dayong & Yang, Haiquan, 2018. "SAD and stock returns revisited: Nonlinear analysis based on MF-DCCA and Granger test," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 1009-1022.
    2. Wang, Luo-Qing & Xu, Yong-Xiang, 2018. "Distribution of individual status in the invisibility similarity network of new social strata in Shanghai," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 426-434.
    3. Wang, Luo-Qing & Xu, Yong-Xiang, 2018. "Assessing the relevance of individual characteristics for the structure of similarity networks in new social strata in Shanghai," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 881-889.
    4. Zhang, Wei & Wang, Pengfei & Li, Xiao & Shen, Dehua, 2018. "Quantifying the cross-correlations between online searches and Bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 657-672.

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