The Study Of Multifractal Cross-correlation And Its Application On Financial Time Series

In recent years, the multifractal auto-correlation and cross-correlation analysis in complex systems have been extensively studied, ranging from hydrology, meteorology, biological medicine, to sociology, and economic fields. In the paper, we focus on the multifractal cross-correlation analysis and study its application on the financial time series, mainly including:(1) We introduce the classical auto-correlation, cross-correlation coefficient and multifractal detrended cross-correlation analysis of discrete case, generalize it to continuous case;(2) Deduce the superposition formulas of auto-correlation and cross-correlation functions;(3) Employ empirical mode decomposition and Fourier filtering to minimize the effects of external trends on the detection of long-range scaling behavior;(4) We also investigate the effects of time delay on the scaling exponent as well as multifractality;(5) We systematically study the logarithmic return and volatility of Shanghai and Shenzhen stock markets in China;(6) At last, we describe the extreme events of volatility in two markets by two-tuples, i.e. extreme value and return interval. Furthermore, the probability density function of respective variables and their joint probability distribution function are given.