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

Xuebo Li, Xin Hu, Lan Hu, Shenyan Deng, Langxi Zhang and Helin Wu
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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

International Journal of Modern Physics C (IJMPC), 2025, vol. 36, issue 01, 1-13

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.

Keywords: Multi-scale coherence; multifractal analysis; stock market (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0129183124501705

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