混沌时间序列的局域多项式系数建模及预测

Local Polynomial Coefficient AR Prediction Model for Chaotic Time Series

摘要: 由于局域线性模型的简洁、易于实现，在过去的三十年里，它被广泛的研究并用来预测混沌时间序列。本文依据混沌时序的局部特性和非线性特性，在局域线性模型的基础上，提出基于多项式系数自回归模型的局域非线性混沌时间序列预测方法(简称局域非线性模型)。相比于局域线性模型，该模型能够有效地逼近混沌时间序列的非线性特性。三种典型的混沌时间序列(Logistic映射、Henon映射和Lorenz系统)的仿真结果表明，局域非线性模型的多步预测性能及预测稳定性均好于局域线性模型，且在样本数据较少的情况下也有较高的预测精度。

Abstract: The local linear model, being widely studied and used to predict chaotic time series, has a history of over thirty years. Because of its simple structure, it is easy to implement. However, the local linear method cannot effectively fit nonlinear characteristics of chaotic time series. According to the local and nonlinear characteristics of chaotic time series, a local polynomial coefficient autoregressive prediction model is proposed, namely, local nonlinear prediction model, based on local linear model. Compared to the local linear model, local nonlinear prediction model can approximate many effec-tively nonlinear properties of chaotic time series. The simulation results of three typical chaotic time series (Logistic mapping, Henon mapping and Lorenz system) show that prediction performance and stability of local nonlinear multi-step model are better than the local linear model. Moreover, the presented model has higher prediction accuracy, even under the circumstances of less sample data.