China's Stock Market Nonlinear Testing And Modeling

In this study, the time series data of the stock market indices of Shanghai and Shenzhen in recent years are studied, their nonlinear characteristics detected and analyzed and a nonlinear structural model of stock market constructed and compared to real financial market.The existence of nonlinear features in the stock market time series data is first tested with traditional econometric methods. BDS test, autocorrelation test, heteroscedasticity test and GARCH modeling on the return series of different forms show that after excluding linear stochastic process, there still exists a nonlinear process which is mean reverting and coupled with a variance that follows a GARCH model. Moreover, the returns series exhibits typical feature of volatility clustering. Limited by the traditional tests, it cannot be identified whether the nonlinear process is nonlinear stochastic or nonlinear deterministic.Tests of nonlinear features under the framework of nonlinear theories are then employed through methods of phase space reconstruction. Methods of false nearest neighborhood and mutual information are adopted to first reconstruct the return series. based on which chaos is detected:the correlation dimension of the return series of both Shanghai and Shenzhen stock market indices is around five, increasing with the embedding dimension but significantly less quickly, which implies a high dimensional structure. The Lyapunov Exponents are also both positive, which shows the chaotic characteristic of sensitiveness to initial conditions in a deterministic process. This study proceeds to obtain Hurst Exponents of the stock markets based on the R/S test of Fractal Theory. They are both around 0.6, which, from the traditional point of view, shows that there exists fractal features and long memory in the time series. A modified R/S test is then introduced to exclude correlation. The modified result rejects the null hypothesis of long memory. Thus, it is concluded that China's stock market is a noisy chaotic system.Then a nonlinear structural model based on Adaptive Belief System is proposed. The BH two-trader type model is expanded to a three-trader type model. The third-type trader who includes more historical information in his trading strategy, of both historical trading volume and price, is introduced. The third-type trader overtakes the two other types in profits in the long run even after information cost is deducted, which shows that with the assumptions of heterogeneity, bounded rationality, adaptive learning and evolutionary interaction in the nonlinear model, technical traders will not be driven out of market that is informationally efficient. Introducing noises into the model, the price series and return series generated by the noisy chaotic dynamic system share similarity with the real financial time series in the phenomena of volatility clustering, which shows that volatility clustering arises as an endogenous phenomenon caused and amplified by the trading process. Based on Chaos Theory and Bifurcation Theory, given different parameter settings, the coexistence of either a steady state and a stable limit cycle or a strange, chaotic attractor and a steady state explains the two mechanisms of price fluctuations. These correspond respectively to weak and strong trend extrapolation.