Multifractal analysis of the Chinese stock, bond and fund markets

The stock, bond and fund markets are three important components of a financial market, and the volatility of the markets and correlations between the markets have been paid extensive attention by researchers and investors. In this paper, we devote our efforts to studying the Shanghai financial market, while the return series of Shanghai Composite Index, Shanghai Bond Index and Shanghai Fund Index are considered. Statistical tests are used to detect the nonlinear auto-correlated structures and long-range cross-correlations of the three time series. The multifractal detrended fluctuation analysis and multifractal spectrum analysis methods are applied, by which the existence of multifractality in these three return series are revealed and the sources of multifractality are explored. In particular, the multiscale multifractal detrended cross-correlation analysis method is employed for the first time to generate the Hurst surfaces, which can be used to visualize the dynamic behaviors of cross-correlations among the markets. Empirical results show that the cross-correlations among the markets present different fractal features at different time scales. Further, our study finds that the correlation between the stock and fund markets is stronger than that of the other two groups, and the correlation between the stock and bond markets is unstable. These findings can help to better understand the dynamic mechanisms that govern the volatility of security markets and aid in performing better financial risk assessment and management.