A Nonlinear Dynamics Study Of The Index Of Shanghai Stock Market

According to the efficient market hypothesis (EMH),the prices of assets in an efficient capital market follow random walk,based on which the modern financial analysis system has been established.Contrary to EMH,the fractal market hypothesis says that the assets'prices of capital market are following the Brownian motion,and have chaotic characteristics.If the fractal market hypothesis holds true in stock market,traditional linear time series analysis methods have no use to detect the chaotic and fractal behaviors,but nonlinear ones can do this job.In this paper,we use nonlinear time series analysis methods to study the index of daily return series of shanghai stock market,and probe into the reasons why the shanghai stock market are chaotic and fractal and the application of the fractal market hypothesis.In this paper,the sample spreads from November 5^th 2007 to March 25^th 2009.First of all,the qualitative analysis is applied on the series.The results shows the differences between market data and the normally distribution random data.The bispectram analysis shows the series are chaotic.After that,some nonlinear characteristic values have been calculated to confirm the chaotic properties.For a chaotic system,the attractor has fractal geometry property.Also,the R/S analysis has been applied to the time series.The analysis shows that the index return series have memory period.From the analysis,the index return series are nonlinear.It can be contradicts that the fractal market hypothesis is true in shanghai stock market,which contradicts the market hypothesis.In the end of this paper,some simple applications of the chaotic and fractal theory are discussed.