Prediction To Multivariate Chaotic Time Series And Its Application To Stock Market

In this dissertation, we mainly study the preferences in the phase-space reconstruction and the prediction methods of the multivariate chaotic time series. Based on the current preferences study, two new computing methods are brought forward after amelioration, which, afterwards, are named with the local multivariate polynomial prediction method and the regularized multivariate local polynomial prediction method. And the emulational results of the multivariate time series of Lorenz system prove that these methods are much more effective and precise than common ones, finally they are applied to predict the composite index time series in Shanghai stock market. The dissertation is arranged as follow:Firstly, the theoretical background and study status quo at present in the field of the applied chaotic time series prediction theories are summarized, and the newest chaotic time series prediction methods are introduced While the theory of the phase-space reconstruction is the base of the chaotic time series prediction methods, the embedding dimension and time-delay are two important parameters in the theory. Therefore, to determine the two parameters, two new computing methods, which can reduce subjectivity in the course of parameters confirmation as the improvement of the false neighbor method and the least prediction error method, are put forward after current preferences methods are studied. And the two new computing methods are proved to be effective by the emulational results of the multivariate time series of Lorenz system.Secondly, on the basis of the phase-space reconstruction theory of multivariate chaotic time series, a local multivariate polynomial prediction method is put forwarded, which is a generalization of local polynomial prediction method of the univariate time series. And the emulational results show that the method advanced here is better than that of the univariate time series. At the same time, the local linear prediction method and RBF method are studied, and a universal linear regression model of the multivariate chaotic time series is summarized, then we...