Study On Correlation Relationships Of Financial Complex Systems

Complex system is a kind of dynamical system. It is always consisted by several subsystems, which have their own statistic characteristics and correlated with each other in some way. It is a difficult task to characterize and understanding complex system. We always study the characteristics of complex system by analyzing time series recording the dynamic procedure in this complex system. In this paper, we first discuss the power-law cross-correlation in the two couple of financial time series with multifractal detrended cross-correlation analysis(MFDCCA). The financial time series are Shanghai Composite Index(SSE) and Shenzhen Component Index(SZSE), Index(SSE) and Hang Seng Composite Index(HSI), which are three representative index in Chinese financial market. As a result, we find that the power-law and cross-correlation relationship existed in both the two couple of time series. To verify the validity and reliability of multifractal detrended cross-correlation analysis(MFDCCA) in analyzing the cross-correlation, two-component Autoregressive Fractional Integrated Moving Average(ARFIMA) is applied to model time series. There is a specific cross-correlation intensity in a couple of ARFIMA series. As a comparison, we calculate the cDCCA coefficient of ARFIMA series and the empirical index. The results show that MFDCCA and σDCCA give similar results and succeed to extract rational cross-correlations, and the description of cross-correlation by σDCCA and ARFIMA are more accurate than MFDCCA.As a general development, we discuss the correlation relationship of more than two time series, coupling multifractal detrended cross-correlation analysis(CMFDCCA) and modified CMFDCCA (CMFDCCA based on sliding windows) are introduced in this paper, we also discuss the coupling correlation relationship of representative index in Chinese financial market (SSE, SZSE, HSI) and American financial market (S&P500, DJIA, NASDAQ). The result shows that power-law and correlations both existed in the two market and the results of CMFDCCA based on sliding windows are better.