Prediction Of Chaotic Time Series Based On Autoregression Model

In many cases there exists chaotic motion. Chaotic motion is disorder and self-similar fractal structure. Chaotic time series is sensitive dependence on initial conditions, the prediction effect of general time series prediction methods is poor, while its self-similar structure makes it possible to predict accurately.The local linear model, being widely studied and used to predict chaotic time series, has a history of over thirty years. It has simple structure, and it’s easy to implement. However, the local linear method cannot effectively fitting nonlinear characteristics of chaotic time series. According to the local and nonlinear characteristics of chaotic time series, a local polynomial coefficient autoregressive prediction model and a local functional coefficient autoregressive model are proposed. Compared to the local linear model, local nonlinear prediction model can effectively approximate nonlinear properties of chaotic time series. The simulation results of three typical chaotic time series(Logistic mapping, Henon mapping and Lorenz system) show that local nonlinear multi-step prediction performance and stability are better than the local linear model. Moreover, the presented models can predict more accuracy, even under the circumstances that less sample data.It’s difficult to detect the weak signal which losts in the chaotic background signal. It is significance and has application value, especially the weak sine signal’s detection and recovery. By studying various detection methods for sine signal in strong background noise, we propose a local linear- Periodogram- Kalman filtering(LL-P-KF) hybrid algorithm. The proposed method turns detection and recovery of sinusoidal signal from original signal into that from error. First, the hybrid signal is phase-space reconstruction, one-step prediction error is obtained by using local linear method; then, we detect sinusoidal signal from error by using periodogram; finally, we use error as a measurement and construct state and measurement equations based on the characteristics of sinusoidal signal and the local linear prediction method, and recover the sinusoidal signal from the error by using Kalman filtering.The hybrid algorithm does not need to know the priori knowledge of the chaotic system dynamics equations and sine signal, and is a simple algorithm to detect and recover sine signal. Simulation results show that the hybrid algorithm has better recovery results.