Study On The Fractal Character Of Our Country Stock Market And GARCH Family Models Of The Price

Today the nonlinear model is more applicable than linear model. The demonstrations indicate that the capital market theory based on linear model can't correctly show the essence of security market. The nonlinear model believes that the influence factors are very complicated and the mentalities of the investor influence the price. The fluctuation of the price is fractal brown movement and has the characteristic of fractal and chaos.The article analyses whether the theory of EMH market can explain some phenomena on capital market. We provide some evidence for the non-normal, non-gaussian distribution, auto-correlation, non-linear and heteroskedasticity character of stock price. We test the fractal of our security market by the way of R/S, and compute the Hurst Exponent which is bigger than 0.5, the length of memory is between 200days and 400days and the Lyapunov exponent converge on the biggest Lyapunov exponent. This paper shows the linear model of time sequence and the ARCH model and finds that the GARCH model could describe the fluctuation of price in some degrees. In our country the figure of news impact curves is contrary to other countries because of the short of sell system.The stock price is complicated because the investor has the property of complication. The investor should adopt different investment strategy in different conditions.