Correlation analysis of multifractal stock price fluctuations based on partition function

Studying the correlation analysis of stock price fluctuations helps to understand market dynamics better and improve the scientific nature of investment decisions and risk management capabilities. Most existing methods use multifractals to explore the correlation between different economic entities. However, the study of multifractals fails to fully consider the weight of each entity’s impact on the market, resulting in an inaccurate description of the overall market dynamics. To address this problem, this paper creatively proposes a weighted multifractal analysis method (WMA). The correlation analysis of government regulation, market supply and demand, and stock price index is performed using the data of A-share listed companies in Shenzhen and Shanghai as samples. First, we consider the amplitude fluctuation information the signal carries and weigh the partition function according to the proportion of variance in the segment for different amplitude changes. Secondly, we derive the theoretical analytical form of the classical multifractal model (SMA) of the scaling indicator under WMA. Finally, through numerical simulation experiments, it is confirmed that WMA is equally effective as SMA. In addition, the re-fractal correlation analysis of real financial time series also confirms that WMA can effectively utilize the amplitude fluctuation information in the series and outperforms the classical SMA method in distinguishing different signals.