Prediction To Chaotic Time Series And Its Application To Stock Market

In this dissertation, we mainly study the prediction methods to chaotic time series and improve the efficiency from three different aspects. Then the methods are applied to theoretical chaotic models and Shanghai stock market. This dissertation consists of the following parts:At first, the characters and developments of complexity and nonlinear analysis such as chaos are summarized and their applications to stock markets are also summed up. Then some problems in the present research of chaotic prediction and the direction for further study in this field are illuminated.Secondly, the theory of prediction is discussed and the several prediction methods that are often used at present are introduced, such as local constant prediction, local linear prediction and neural network prediction. And the relationship of prediction and noise is further discussed. Thirdly, prediction methods to multivariate chaotic time series are studied, based on the above univariate prediction methods. Under the same circumstances such as the same data length, numerical emulation calculations verify that multivariate time series can predict better than univariate time series both with local prediction methods and with global ones.Fourthly, as to the time series from stock markets, different detrending methods are studied and their different effects on the prediction are analysis. Finally, connecting embedding theory with prediction errors, we propose a new prediction method to chaotic time series based on embedding technique and prediction errors on tested sets. This method makes full use of the advantages of the two aspects and overcomes their own disadvantages. Therefore it can predict better.