Fractal Interpolation Analysis Of China's Stock Market Index

Based on relevant research of the Fractal Market and Fractal Time Series theory, the author chooses the theory of fractal interpolation raised by M.F.Barnsley for further research, and make empirical analysis through Fractal interpolation method for the index of Shanghai stock market and Shenzhen stock market. The period of the data collected and analyzed is from 1998 to 2009. The self-similarity of the index changes in Shanghai and Shenzhen stock market is analyzed.Firstly, Kurtosis and Skewness 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 of Fractal Time Series and its important features, the rescaled range analysis(R/S analysis) are analyzed and long-range correlation of Shanghai stock market and Shenzhen stock market are confirmed. The length of long-range correlated time is given.On the basis of normality test and Fractal Time Series analysis, this paper has further established the fractal interpolation model of the index of Shanghai stock market and Shenzhen stock market and has discussed the fitting effect of it. Finally, combining the analysis and research above, we make a prediction of the index trend of Shanghai stock market by using fractal interpolation and analyze the effectiveness of this forecasting method.