Research And Application Of Rescaled Range (R/S) Analysis In Fractal Characteristic Of Stock Market

Fractal and Chaos theories are among the most advanced sciences in the world. The application of Rescaled Range (R/S) analysis in fractal characteristic of security market is researched in this paper. Firstly, ARMA model is used to regress a series to recede linear depending. Then R/S analysis is used to analyze the series has been receded linear depengding. It proves that R/S analysis is a stable method to find the nonlinear depending in system. Secondly , by using Matlab and Excel sofewares, closing quotation datas of aggregative index number of Shanghai Security Market is analyzed by R/S analysis. It proves that Stock Market isn't obey normal distribution and is a random walk with deviation.A non-periodeic cycle is finded in stock market by regressing the date. Using V-Stastistic can calculate the length of this non-periodeic cycle. It exist many kinds of noise in stock market, R/S analysis is used to analysed series with noise in order to analyze if it is still efficient to the series with noise .R/S Analysis can find the nonlinear depending and the non-periodeic cycle in process with noise,it proves that R/S Analysis is stable for noise .At last, BDS stastistic is used to prove that stock market in China is not an independent process but a process with two dimention correlation in futther. Stock market in china is not an efficient market.The conculsion in this paper can faithfully evaluated the fractal characteristic of stock market in China.So this method can provide appropriate advices for investors in stock market.