TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecasting

Peiyuan Liu, Beiliang Wu, Yifan Hu, Naiqi Li, Tao Dai, Jigang Bao, Shu-Tao Xia
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:39815-39840, 2025.

Abstract

Non-stationarity poses significant challenges for multivariate time series forecasting due to the inherent short-term fluctuations and long-term trends that can lead to spurious regressions or obscure essential long-term relationships. Most existing methods either eliminate or retain non-stationarity without adequately addressing its distinct impacts on short-term and long-term modeling. Eliminating non-stationarity is essential for avoiding spurious regressions and capturing local dependencies in short-term modeling, while preserving it is crucial for revealing long-term cointegration across variates. In this paper, we propose TimeBridge, a novel framework designed to bridge the gap between non-stationarity and dependency modeling in long-term time series forecasting. By segmenting input series into smaller patches, TimeBridge applies Integrated Attention to mitigate short-term non-stationarity and capture stable dependencies within each variate, while Cointegrated Attention preserves non-stationarity to model long-term cointegration across variates. Extensive experiments show that TimeBridge consistently achieves state-of-the-art performance in both short-term and long-term forecasting. Additionally, TimeBridge demonstrates exceptional performance in financial forecasting on the CSI 500 and S&P 500 indices, further validating its robustness and effectiveness. Code is available at https://github.com/Hank0626/TimeBridge.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-liu25cb, title = {{T}ime{B}ridge: Non-Stationarity Matters for Long-term Time Series Forecasting}, author = {Liu, Peiyuan and Wu, Beiliang and Hu, Yifan and Li, Naiqi and Dai, Tao and Bao, Jigang and Xia, Shu-Tao}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {39815--39840}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/liu25cb/liu25cb.pdf}, url = {https://proceedings.mlr.press/v267/liu25cb.html}, abstract = {Non-stationarity poses significant challenges for multivariate time series forecasting due to the inherent short-term fluctuations and long-term trends that can lead to spurious regressions or obscure essential long-term relationships. Most existing methods either eliminate or retain non-stationarity without adequately addressing its distinct impacts on short-term and long-term modeling. Eliminating non-stationarity is essential for avoiding spurious regressions and capturing local dependencies in short-term modeling, while preserving it is crucial for revealing long-term cointegration across variates. In this paper, we propose TimeBridge, a novel framework designed to bridge the gap between non-stationarity and dependency modeling in long-term time series forecasting. By segmenting input series into smaller patches, TimeBridge applies Integrated Attention to mitigate short-term non-stationarity and capture stable dependencies within each variate, while Cointegrated Attention preserves non-stationarity to model long-term cointegration across variates. Extensive experiments show that TimeBridge consistently achieves state-of-the-art performance in both short-term and long-term forecasting. Additionally, TimeBridge demonstrates exceptional performance in financial forecasting on the CSI 500 and S&P 500 indices, further validating its robustness and effectiveness. Code is available at https://github.com/Hank0626/TimeBridge.} }
Endnote
%0 Conference Paper %T TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecasting %A Peiyuan Liu %A Beiliang Wu %A Yifan Hu %A Naiqi Li %A Tao Dai %A Jigang Bao %A Shu-Tao Xia %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-liu25cb %I PMLR %P 39815--39840 %U https://proceedings.mlr.press/v267/liu25cb.html %V 267 %X Non-stationarity poses significant challenges for multivariate time series forecasting due to the inherent short-term fluctuations and long-term trends that can lead to spurious regressions or obscure essential long-term relationships. Most existing methods either eliminate or retain non-stationarity without adequately addressing its distinct impacts on short-term and long-term modeling. Eliminating non-stationarity is essential for avoiding spurious regressions and capturing local dependencies in short-term modeling, while preserving it is crucial for revealing long-term cointegration across variates. In this paper, we propose TimeBridge, a novel framework designed to bridge the gap between non-stationarity and dependency modeling in long-term time series forecasting. By segmenting input series into smaller patches, TimeBridge applies Integrated Attention to mitigate short-term non-stationarity and capture stable dependencies within each variate, while Cointegrated Attention preserves non-stationarity to model long-term cointegration across variates. Extensive experiments show that TimeBridge consistently achieves state-of-the-art performance in both short-term and long-term forecasting. Additionally, TimeBridge demonstrates exceptional performance in financial forecasting on the CSI 500 and S&P 500 indices, further validating its robustness and effectiveness. Code is available at https://github.com/Hank0626/TimeBridge.
APA
Liu, P., Wu, B., Hu, Y., Li, N., Dai, T., Bao, J. & Xia, S.. (2025). TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecasting. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:39815-39840 Available from https://proceedings.mlr.press/v267/liu25cb.html.

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