Analysis of noisy chaotic time series prediction error

For the noisy chaotic series prediction problem, traditional methods are quite empirical, and are lacking in the analysis of the composition of the prediction error, thereby ignoring the the difference between chaotic dynamics reconstruction and prediction model. Based on the composition of actual prediction error, the predictor bias error and input disturbance error are defined in this paper and two kinds of global forecasts, ensemble least-square method and regularization method are analysed. It is shown that the ensemble least-square method is suitable for the reconstruction of chaotic dynamics, but has a greater influence on the predictor error. On the other hand, the regularization method can improve the sensitivity of the predictor, but it can be influenced by the input perturbation error. Two simulation examples are used to demonstrate the difference between the chaotic dynamical reconstruction and the establishment of prediction model, and to compare the ensamble least-square method and the regularization method, and at the same time indicate that the actual prediction error is influenced both by the input disturbance error and by the predictor error. In practice, a balance should be stricken between the two, in order to optimize the model prediction accuracy.