Multifractal Statistical Analysis of Financial Time Series

Based on the multifractal theory, this paper presents an empirical research on the data of the closing prices of Shanghai Stock Price Index from 1990 to 2005. Firstly, by transferring the time series into multifractal spectra plots, it confirms the existence of multifractal phenomenon in Shanghai stock market. Secondly, it analyzes statistically the correlations between the parameters of the multifractal spectra (the width of the multifractal spectrum and the difference of the fractal dimensions of the maximum and the minimum probability subsets) and the variation of the closing index, the logarithmic return and the gain probability. It indicates that the multifractal analysis can reveal insightful information about the market trend.