含噪混沌时间序列预测误差分析

Analysis of noisy chaotic time series prediction error

对于含噪混沌时间序列预测问题,传统方法存在较大的经验性,对预测误差的构成分析不足,因而忽略了混沌动态重建与预测模型建立之间的差异性.本文将实际预测误差分解为预测器偏差和输入扰动误差,并对整体最小二乘和正则化两种全局预测方法进行分析比较,进而说明整体最小二乘适用于混沌动态的重建,对预测器偏差影响较大,而正则化方法能够改善预测器敏感性,对输入扰动误差影响较大.通过两个仿真实例,展示了混沌动态重建与预测模型建立之间的差异,在对比最小二乘和正则化方法的同时验证了实际预测误差受预测器偏差和输入扰动误差共同作用.并指出,在实际操作时应在二者间寻求平衡,以便使模型预测精度达到最优.

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.