The Properties Study In Multifractal Process

With the development of nonlinear science, more and more scholars use of fractal theory to study the nonlinear phenomenon of financial market price fluctuations. Local indepen-dence of multifractal model of asset returns is proved in this paper, while the fractal theory was used to empirical research on the stock market. In addition to introduction and conclu-sion and prospect in chapter 4, there are mainly the following three parts in this paper:Part 1 contains different fractal models and their properties; In part 2, we studied the fractal characteristic of stock market based on empirical research, fractal market theory can explain the phenomenon which efficient market hypothesis can't to explain, unifractal anal-ysis mainly consider the long-range dependence and Hurst exponent of financial time series, we used classic and modified R/S method to test the long-range dependence of Shanghai Composite day and week closing index logarithmic rate of return, and calculate the Hurst exponent, by comparing the fractal characteristic of different time scale sequence, we can obtain the features of statistical self-similarity and scale invariance in stock market, at the same time, we employed sliding window multifractal detrended fluctuation analysis method and multifractal detrended moving average method to analyzed the multifractal structure of stock market; In part 3, local independence of multifractal model of asset returns is proved under certain condition.