Study Of Chaotic Time Series Prediction Methods

Chaos is a pseudo-random phenomenon exhibited by a deterministic dynamical system and it involves in various fields of natural and social sciences. Chaos has always been the focus of scientific research in the area of nonlinear science. The prediction of chaotic time series, which has extensive applications is an important branch in the field of chaos. With the low-dimensional chaotic time series prediction becomes more and more mature, the attention has turned to the prediction of high-dimensional chaotic systems, in which the prediction of spatio-temporal chaotic system has a great significance.The definition of chaos is always a controversial question in the scientific field. We describes one of the most widely used definition that is Li-Yorke definition. After describing the significance of the prediction of chaotic time series, we discusses whether a given sequence is chaotic or not according to qualitative and quantitative methods. Every method is demonstrated by simulations. Prediction of chaotic time series is the focal point of this thesis. Since reconstructing the phase space is necessary for most prediction methods, the phase space reconstruction method is expounded and especially, the choice of optimal embedding dimension and time delay is discussed in detail. Simulations are carried out to demonstrate our analyses. When studying prediction methods of low-dimensional chaotic time series (conventional chaotic time series), we give a large number of simulations to compare the prediction performance of three methods in noise and noise-free environment, i.e., the methods of local prediction, global prediction and adaptive prediction. When studying the prediction method of high-dimensional chaotic system, a non-parametric kernel estimation method is used to predict the spatio-temporal chaos. Simulations verify the effectiveness of the algorithm. Finally, this paper summarizes the above prediction methods to provide a foundation for future research.