Fractal Features And Quantitative Strategy Of China's Stock Market Based On Fractal Theory

China's market is not a balanced linear systems,but has the fractal characteristic of nonlinear complex system,the fractal theory has a wide adaptability to describe nonlinear characteristics.Therefore,this thesis attempts to analyze the fractal characteristics of China's stock market in different dimensions from micro to macro under the background of fractal market theory.This thesis is represented by the Shanghai Composite Index,the CSI 300 and the Shenzhen Component Index.It is shown that the sample data has the nature of thick tails and sharp peaks through self-similarity test,J-B tests,Q-Q plot tests and other methods in turn.From the macro perspective.Firstly,the Hurst indices of sample data on daily scale,weekly scale and monthly scale are estimated from single dimension by R/S analysis and DFA analysis,which proves the existence of long-term memory of the three indices and finds that the characteristics of long-term memory of Shanghai stock market are more significant.Secondly,based on V series measurement method,the length of non-cyclic index is 250 days and BB model is used to measure the peaks and troughs of China's stock market to distinguish the bull and bear markets.At last,with the help of time-varying Hurst index,it is found that the conversion of bull and bear market at the closing price of the index is accompanied by the maximum or minimum value of Hurst index.From the microcosmic point of view,H(q)of different order q is calculated by MF-DFA analysis under multiple dimensions,and the inhomogeneity of internal structure of China's stock market is proved by combining wave function,scale function and multifractal spectrum,and the singularity of Shanghai stock market is greater than that of Shenzhen stock market.It is confirmed that the stock market has multiple fractal structural characteristics and the yield sequence fluctuates when the yield sequence fluctuates.The closer the time-varying Hurst index is 1,and when the yield sequence fluctuates greatly,the closer the time-varying Hurst index is 0.At the end of the thesis,Hurst index is used as a quantitative index to construct timing strategy to simulate trading,the comparison between Hurst index timing strategy and double moving average timing strategy shows that the Hurst index timing strategy has better performance in winning rate,cumulative return rate and average return rate.