基于小波分解和残差GM(1,1)-AR的非平稳时间序列预测

Non-stationary time series prediction based on wavelet decomposition and remanet GM(1,1)-AR

提出基于二进正交小波变换和残差GM(1,1)-AR方法的非平稳时间序列预测方案.首先利用Mallat算法对非平稳时间序列进行分解和重构,分离出非平稳时间序列中的低频信息和高频信息;然后对高频信息构建自回归模型,对低频信息则用灰色残差模型进行拟合;最后将各模型的预测结果进行叠加,从而得到原始序列的预测值.该方法不仅能充分拟合低频信息,而且可避免对高频信息的过拟合.实验结果表明,这种方法比传统的非平稳时间序列预测方法具有更高的预测精度.

A non-stationary time series prediction method based on wavelet transform and remanet GM（1,1）-AR was proposed.By wavelet decomposition and reconstruction,the non-stationary time series were decomposed into a low frequency signal and several high frequency signals.The high frequency signals were predicted with auto-regression models,and the low frequency was predicted with remanet GM（1,1）.The prediction result of the original time series was the superimposition of the respective prediction. This new method avoids the over-fitted for high frequency signals,and adequately fits the low signal of the non-stationary time series,so better predicting performance can be obtained.Experiments show the novel method is of higher accuracy in comparison with the traditional ones.