基于提升方案的冗余Haar小波变换与时间序列预测

针对小波分析存在的边界问题，提出一种基于提升方案的冗余Haar小波变换(Haar_RLWT)。使用该方法得到的系数序列，在具备时移不变性的同时，消除了右侧边界存在数据畸变的现象，使小波分析技术结合神经网络等传统预测模型的方法应用于时间序列预测任务具备可行性。同时为进一步提高预测效果，引入神经网络集成技术以改善网络泛化能力。实验表明，该综合预测模型预测效果与稳定性优于传统预测模型。

Redundant Haar wavelet transform and time series forecasting based on improved lifting scheme

In the view of the boundary problem of wavelets analysis method,a redundant Haar wavelet transform based on Lifting Scheme(Haar_RLWT) was proposed.The wavelet coefficient sequences decomposed by this new method possessed time-invariant capability and eliminated the data distortion phenomenon around right boundary,which made it feasible that the traditional forecasting models such as Neural Networks combined with wavelets analysis can be applied to the time series forecasting task.Furthermore,the application of Neural Network Ensembles improved network generalization and enhanced the forecasting performance.Experiments stipulate that the forecasting effect and rousting of the hybrid forecasting model is superior to traditional forecasting models.