Study On Fractal Methods And Its Application To China's Stock Market

In this dissertation, the long-range correlation behaviour in China's stock market is systematically studied by the latest fractal methods of time series. The materials are from daily closing indexes in the Shanghai stock market for the period 1990.12.19-2002.5.14, and daily closing indexes in the Shenzhen stock market for the period 1991.4.3-2002.5.14. Firstly, the introduction of this problem and the progress of fractal methods in different research fields are summarized. Then, frequency histgram,P-P Normal Probablity Plots,Q-Q Normal Probablity Plots,Kurtosis and Skewness testing, and Jarque-Bera testing, are used to Shanghai stock market and Shenzhen stock market, finding out that they are not the efficient market. Therefore, the necessity for using fractal methods to study China's stock market are presented. After explaining correlation theory and its important features, the rescaled range analysis,modified rescaled range analysis and detrended fluctuation analysis are analysed. As for the drawbacks produced by the rescaled range analysis when faced with short term correlation, a modified rescaled range analysis based on short term correlation model is applied to Shanghai stock market and Shenzhen stock market. The result is explained and compared. For the fractal behavior of Shanghai stock market and Shenzhen stock market cannot be completely depicted by the monofractal analysis methods, the height-height correlation function,structure partition function and multifractal detrended fluctuation analysis are used. Through their application on Shanghai stock market and Shenzhen stock market , the conclusion is that China's stock market has the multifractal feature. All these different information on differentscales plays an important role in financial risks management.