In this paper, time series with stable convergence, saddles, Hopf bifurcations and chaotic points in one kind of complicated systems have been studied in respects of： fractal characteristic and fractal dimension. By using phase space reconstruction technology of chaotic time series, work of reconstruction has been done respectively on these four different conditions and further by applying wavelet network models, work of modeling and prediction have been done accordingly. The results indicate： treatment of zero mean value in the identification of the chaotic models has no obvious influence on precision and length of predictions, while the treatment by Fourier Filter can damage effectiveness of prediction.
This paper takes the Shanghai Security market stock composite index as the research object, analyzes its intrinsic fractal essence characteristics by the application of fractal theory and the method, and computes the Hurst index, fractal dimension and correlated function of the highest prices of the complex index. Moreover, it studies characteristics of long term memory of the sample data and its variance along with time; study existence of chaotic attractors in data of the complex index by reconstructing the phase space of the index data. Finally, this paper carries on the related forecast demonstration study to the stock composite index. Results of the study have certain reference function to the actual problem.
In this paper, 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. This is done first by reconstructing a phase space using chaotic time series, then using K-entropy as a quantitative parameter to obtain the maximum predictability time of chaotic time series, finally the predicted chaotic time series data can be acquired by using RBFNN. The application considered is Lorenz system. 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.
