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.

doi: 10.16186/j.cnki.1673-9787.2024070018

Received: 2024/07/03

Revised: 2024/10/29

Published: 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