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

作　　者：张华[1] 任若恩[1] 

机构地区：[1]北京航空航天大学经济管理学院,北京100191

出　　处：《系统工程理论与实践》2010年第6期1016-1020,共5页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金创新研究群体科学基金(70821061)

摘　　要：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.

关 键 词：小波分解 非平稳时间序列 残差GM(1 1)模型 自回归 预测 

分 类 号：F201[经济管理—国民经济]