Study On The Non-linear Characteristics And Trend Of The China Stock Market

The people's understanding of stock market is built on the modern capital market theory, the modern capital market theory is based on the Efficient Market Hypothesis. the random walk is premise of the EMH and contains the norm distribute. However, a lot of studies show that the capital market different with the norm distributes. Undoubtedly this is huge shock to the modern capital theory. Focusing on the data of Chinese stock market, uses nonlinear time series analysis method to a more comprehensive study and to test the chaos phenomena in Chinese stock market in this paper.The Shanghai Stock Composite Index and the Shenzhen Stock Component Index are studied in this paper, sample periods of which spreads from December 16th 1996 to December 30th 2006, use log-linear de-trending methods to time series, make the time series smooth in nonlinear time series analysis. First of all, qualitative analysis is applied on the index time series. By the frequency distribution statistics, differences have been found between index data and the normally distributed random data. Use power spectra and PCA show that there are nonlinearities in the two time series. Then, some nonlinear characteristic values of the two time series have been calculated. The delay times is calculated by average mutual information method, the best embedding dimension is calculated by Cao method. In this base, the calculation results show that the correlation dimensions of Shanghai and Shenzhen index data are 2.4151 and 2.5171 respectively; the Kolmogorov entropies are 0.011 and 0.0075; the maximum Lyapunov exponents are 0.0096 and 0.0059. Compared with the common form of movement characteristics show that the Shanghai Stock Composite Index and the Shenzhen Stock Component Index time series are in chaos state.From the above analysis to study the development trend of the stock market, use method of chaos predict—Volterra series adaptive forecasting model to short forecast of index time series, compared with the results of Local predict and Linear predict, Found Volterra predict result show that there are high precision.