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CHEN X, ZHANG J W, WANG S Y, et al. Multivariate long-term time series prediction based on the lifting wavelet transform [J]. Journal of Henan Polytechnic University (Natural Science) , 2025, 44(4): 66-73.

基于提升小波变换的多变量长时间序列预测

陈旭1, 张建伟1, 王叔洋2, 景永俊1

1.北方民族大学 计算机科学与工程学院，宁夏 银川  750000；2.北方民族大学 电气信息工程学院，宁夏 银川  750000

摘要: 目的 为解决多变量长时间序列预测模型难以充分利用时间序列时频信息的问题，提出一种基于多级提升小波变换的神经网络模型（multi-level wavelet transform Network，mLWTNet）。   方法 首先通过提升小波变换从时域和频域角度对时间序列进行有效分解，并对分解得到的高频子序列进行自适应滤波；其次利用Elman神经网络提取时间序列的非线性特征，同时通过差分自回归移动平均模型（autoregressive integrated moving average model，ARIMA）捕获时间序列的线性特征；最后将非线性与线性预测结果加权融合，以提高预测的准确性。   结果 在5个公开真实数据集上实验结果表明，与FEDformer，InParformer，WaveForM等5种主流的长时间序列预测模型相比，mLWTNet在不同预测长度下的MSE和MAE均达到最优。相比次优结果，mLWTNet的平均MSE和MAE分别提升了约7.15%和2.43%。   结论 通过利用提升小波变换与分层重构预测，能够充分利用时间序列的时频信息，有效提高了时间序列的预测精度。 

关键词:长时间序列预测;时间序列分解;提升小波变换;自适应滤波;Elman神经网络

doi: 10.16186/j.cnki.1673-9787.2024070018

基金项目:中央高校基本科研业务费专项项目（2023ZRLG13）；宁夏回族自治区重点研发项目（2023BDE02017）

收稿日期:2024/07/03

修回日期:2024/10/29

出版日期:2025/06/19

Multivariate long-term time series prediction based on the lifting wavelet transform

Chen Xu1, Zhang Jianwei1, Wang Shuyang2, Jing Yongjun1

1.School of Computer Science and Engineering， North Minzu University， Yinchuan  750000， Ningxia， China； 2.School of Electrical and Information Engineering， North Minzu University， Yinchuan  750000， Ningxia， China

Abstract: Objectives To address the challenge of effectively exploiting time-frequency information in multivariate long-term time series prediction models， this study proposes a neural network model based on multi-level lifting wavelet transform （mLWTNet）. Methods The proposed model first applies the lifting wavelet transform to decompose time series data from both time and frequency domains， followed by adaptive filtering of the resulting high-frequency subseries. Nonlinear features are extracted using an Elman neural network， while linear components are captured with an autoregressive integrated moving average （ARIMA） model. The outputs of the nonlinear and linear predictors are then fused through weighted integration to enhance prediction accuracy. Results Experiments conducted on five publicly available real-world datasets demonstrate that mLWTNet achieves consistently superior performance—measured by mean squared error （MSE） and mean absolute error （MAE）—across various prediction horizons， outperforming five state-of-the-art models including FEDformer， InParformer， and WaveForM. On average， mLWTNet improves MSE and MAE by approximately 7.15% and 2.43%， respectively， compared with the second-best method. Conclusions By leveraging lifting wavelet transform and hierarchical reconstruction-based prediction， the proposed model effectively utilizes the time-frequency characteristics of time series data， significantly improving forecasting accuracy. 

Key words: long-term time series prediction; time series decomposition; lifting wavelet transform; adaptive filtering; Elman neural network