Chaotic Time Series Prediction Method And Its Application

Chaos is an irregular behaviour which is a wide existent phenomenon. Chaos is a complicated behaviour which is from a deterministic nonlinear dynamical system. Phase space reconstruction is the base of using dynamical methods to analyse nonlinear time series. The key of phase space reconstruction is the estimation of its parameter. In this paper we discuss the theory and methods of phase space reconstruction and methods of choosing embedding dimension and delay time.Singular value decomposition is essentially a linear method based on the covariance matrix which reflects the linear dependence. Numerical experience led several researchers to express some doubts about the reliability of SVD. In this paper the matrix constructed by high-order statistics function instead of correlation function is used to improve the method of SVD. Methods used high-order statistics function to construct matrixes is studied and the best two methods are found. When two parameters of four-order cumulant function choose values of the diagonal direction and the off-diagonal direction of the matrix and the third parameter is zero, we can get the best matrix. In this paper we illustrate this method to analyze chaotic time series from Henon attractor and Lorenz model. Simulation results show the validity and the stability of the improved method. And this method is fit for the small set nonlinear time series and is computationally efficient.Chaotic time series are extremely sensitive to its initial conditions. The change of the initial value will be expanded in the rate of exponent. So it is very difficult to predict chaotic time series. But chaos is a deterministic system determined by the nonlinear dynamical mechanism. There is a deterministic rule in the interior of the chaotic system which is seemed as a random move. So chaotic time series can be predicted in the short term. In this paper we analyse the existing prediction methods. And simulation results show the prediction performance of the existing prediction methods.Based on the short-term predictability of chaotic time series and the adaptivetracking chaotic trajectory of adaptive algorithm, a new multi-step-prediction method is proposed in this paper, and this method is used to improve the adaptive prediction method and the local adaptive prediction method. Simulation results show that the multi-step prediction performance of the improved method is rapidly improved. This result is very important to newly understand the predictability of chaotic time series.A number of research show that there is chaotic phenomenon in stock data. In this paper we attempt to apply the phase space reconstruction theory and prediction methods to stock data, and this method's multi-step-prediction performance is better than the previous algorithm's.