Study On Some Problems Of Chaotic Time Series Analysis And Its Application

With the development of nonlinear chaotic dynamic, there are more profound recognitions to the complexity of time series. Especially the analysis of time series is becoming an important research aspect. The analyses of chaotic time series include identification of chaotic characteristic parameter and prediction of chaotic time series, and so on. Because chaotic phenomenon widely exists in nature, the analysis of chaotic time series is more important in the field of chaotic identification and prediction on many dynamic systems.The identification and prediction of chaotic time series are researched in the paper. The main contents are as follows:1. The fractal dimension of time series of classical chaotic systems is firstly confirmed by Takens'estimator method. Then Takens'estimator method is compared with G-P method, it shows that Takens'estimator method inherits all virtues of G-P method and has better characteristics than G-P method such as low computation complexity and fast calculation speed. The fractal characteristics of opening quotation, closing quotation, maximum price and minimum price in Shanghai stock market are calculated by Takens'estimator method. The results demonstrate that the fractal dimension of Shanghai stock data has increasing trends with time. To further prove the chaotic behaviors of Shanghai stock data, the maximum Lyapunov exponent is calculated by the approach of small data sets. The results also indicate that Shanghai stock data are a feeble chaotic system that is in low degree of freedom.2. The maximum predictability time of chaotic time series is studied on the basis of Kolmogorov entropy theory. Then a method of direct multi-step prediction of chaotic time series is proposed, which is based on Kolmogorov entropy and radial basis functions neural networks. And the Lorenz system is predicted by the method. Simulation results for direct multi-step prediction method are compared with recurrence multi-step prediction method. The results indicate that the direct multi-step prediction is more accurate and rapid than the recurrence multi-step prediction within the maximum predictability time of chaotic time series. So, it is convenient to forecast and control with real time using the method of direct multi-step prediction. 3.Agricultural machine power is forecast by diagonal recurrent neural network (DRNN) forecasting model, which is combined the characteristic of global random search of genetic algorithm with the virtue of robust and self-study for nonlinear data of DRNN and agricultural machine power data in history is analyzed by time series. The forecasting results is compared with verify data, that prove the forecasting model in this paper has higher precision.4. A local-region linear prediction method based on radial basis function neural net is presented for chaotic time series prediction, which theory foundation is add-weighted one-rank local-region single-step method. The prediction method is built by using RBFNN substitute for add-weighted one-rank model. The Logistic map and the three axes of Lorenz system are applied to verify the method. Simulation results indicate that the method is effective for prediction of chaotic time series.