Nonlinear Analysis of the U.S. Stock Market: From the Perspective of Multifractal Properties and Cross-Correlations with Comparisons

This study investigates the multifractal properties of daily returns of the Standard and Poor’s 500 Index (SPX), the Dow Jones Industrial Average (DJI), and the Nasdaq Composite Index (IXIC), the three main indices representing the U.S. stock market, from 1 January 2005 to 1 November 2024. The multifractal detrended fluctuation analysis (MF-DFA) method is applied in this study. The origins of the multifractal properties of these returns are both long-range correlation and fat-tail distribution properties. Our findings show that the SPX exhibits the highest multifractal degree, and the DJI exhibits the lowest for the whole sample. This study also examines the multifractal behaviors of cross-correlations among the three major indices through the multifractal detrended cross-correlation analysis (MF-DCCA) method. It is concluded that the indices are cross-correlated and the cross-correlations also exhibit multifractal properties. Meanwhile, these returns exhibit different multifractal properties in different stages of the market, which shows some asymmetrical dynamics of the multifractal properties. These empirical results may have some important managerial and academic implications for investors, policy makers, and other market participants.