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

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.