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Scaling laws of multi-scale coherence and multifractal analysis in the stock market

Author

Listed:
  • Xuebo Li

    (School of Science, Chongqing University of Technology, Chongqing 400054, P. R. China2Center of Spatio-Temporal Big Data Research, Chongqing University of Technology, Chongqing 400054, P. R. Chinaxbl@cqut.edu.cn)

  • Xin Hu

    (School of Science, Chongqing University of Technology, Chongqing 400054, P. R. China)

  • Lan Hu

    (School of Science, Chongqing University of Technology, Chongqing 400054, P. R. China)

  • Shenyan Deng

    (School of Science, Chongqing University of Technology, Chongqing 400054, P. R. China)

  • Langxi Zhang

    (School of Science, Chongqing College of Finance and Economics, Chongqing 400054, P. R. China)

  • Helin Wu

    (School of Science, Chongqing University of Technology, Chongqing 400054, P. R. China)

Abstract

In this study, we utilize the coherence spectrum and structure-function methods to examine the multi-scale coherence and multifractal characteristics of financial time series. The phase spectrum reveals the temporal shift between two indices, indicating whether one leads or lags by several days within a region of high correlation that is scale-dependent. This information can serve as a predictive model for quantitative analysis. The Fourier power spectrum and scaling exponents, derived from the structure-function method, exhibit universal patterns across indices from various countries. Our findings suggest that stock market indices display behavior akin to turbulence, as demonstrated by the structure-function, power-law scaling and multifractal movements. Our results suggest that the fluctuations of indices could be accurately represented by a multifractal random walk model, offering a complex and insightful view of the financial market.

Suggested Citation

  • Xuebo Li & Xin Hu & Lan Hu & Shenyan Deng & Langxi Zhang & Helin Wu, 2025. "Scaling laws of multi-scale coherence and multifractal analysis in the stock market," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-13, January.
    • Handle: RePEc:wsi:ijmpcx:v:36:y:2025:i:01:n:s0129183124501705
    DOI: 10.1142/S0129183124501705
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