自适应局部线性化法预测混沌时间序列

Adaptive Local Linear Predicting Chaotic Time Series

提出一种基于奇异值分解最小二乘法的自适应局部线性化预测方法.它要求数据矩阵的条件数不大于给定阈值,并据此自适应地确定当前相空间的维数,然后根据新的嵌入维数重构数据矩阵,进行模型的参数估计和计算当前预测值.实验结果说明所提方法精度高且稳健.特别是当嵌入维数接近最邻近向量的数目时,其性能显著优于普通局部线性化方法.

Local linear is a well-known method for prediction chaotic time series. there are two shortages: Robustness of the method is poor; it is difficult to determine the embedding dimensions. An adaptive local linear method is proposed, which based on singular value decomposition. The method can determine the crisp embedding dimension adaptively according to singular values of data matrixes, then the new data matrixes are reconstructed, and the parameters of the models are estimated, finally, crisp prediction value is estimated. Noisy Lorenz time series and stock price movements time series are employed to compare proposed approach with original local linear method respectively. Experimental results show that proposed approach is robust, and possessed higher prediction precision than that of original local linear, especially in situations where the selected embedding dimension is close to the number of the nearest neighbors.