• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.3
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• pp.71-87
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• 2024

In this paper, we adopt the MF-DCCA (Multifractal Detrended Cross-Correlation Analysis) method to study the nonlinear correlation between the returns of financial stock markets and investors' sentiment index (SI). The return series of Shanghai Securities Composite Index (SSEC) of China, Shenzhen Securities Component Index (SZI) of China, Nikkei 225 Index (N225) of Japan, and Standard & Poor's 500 Index (S&P500) of the United States are adopted. Firstly, we preliminarily analyze the correlation between SSEC and SI through the Pearson correlation coefficient. In addition, by MF-DCCA, we observe a power-law correlation between investors' sentiment index and SSEC stock market returns, with a significant multifractal correlation. Besides, SI series and SSEC return series have positive persistence. We compare the differences in multifractal cross-correlation between SI and stock return sequences in different markets. We found that the values of SZI-SI in terms of cross-correlation persistence and cross-correlation strength are relatively close to those of SSEC-SI, while the H_xy(2), ∆H_xy, and ∆α_xy of N225-SI and S&P500 are much smaller than those of SSEC-SI and SZI-SI. This reason is related to the fact that the investors' sentiment index originated from the Shanghai Composite Index Tieba. The SI is obtained through natural language processing method. Finally, we study the rolling of H_xy(2) and ∆α_xy. Results indicate that the macroeconomic environment may cause fluctuations in two sequences of H_xy(2) and ∆α_xy.