Research map / Time series / Long-term forecasting
TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecasting
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Proposes TimeBridge, which removes non-stationarity in patch-level intra-variate attention (Integrated Attention) and keeps it in downsampled inter-variate attention (Cointegrated Attention) for long-term multivariate forecasting.
Problem
Non-stationarity in multivariate time series causes spurious regressions in short-term modeling but is needed to reveal long-term cointegration across variates; existing normalization methods either remove or keep it without distinguishing the two regimes.
Approach
Split modeling by horizon: patch-wise detrending before intra-variate attention to avoid spurious short-term regressions, then patch downsampling and channel-wise attention on raw (non-stationary) patch tokens to capture cointegration across variates.
Key results
- Long-term forecasting: averaged over horizons, TimeBridge reports best MSE/MAE on ETTm1 (0.344/0.379), ETTm2 (0.246/0.310), Weather (0.219/0.249), Electricity (0.149/0.245), Traffic (0.360/0.255) and Solar (0.181/0.239) in the hyperparameter-search table.
- Reduces MSE/MAE vs. TimeMixer by 13.66%/7.58% on average across datasets, and vs. ModernTCN by 5.56%/4.12% and DeformableTST by 1.85%/2.49%.
- Financial: on S&P 500 ARR 0.326 and IR 1.842 (best); on CSI 500 ARR 0.285 and ASR 1.405 (best), outperforming iTransformer and Transformer.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use TimeBridge rather than the strongest listed baseline | long-term forecasting · Traffic | MSE: 0.391 -> 0.360 | Helped |
| Use TimeBridge rather than TimeMixer | short-term forecasting · PeMS03 | MAE: 14.63 -> 14.52 | Helped |
| Use TimeBridge rather than TimeMixer | short-term forecasting · PeMS04 | MAE: 19.21 -> 19.24 | Hurt |
| Use TimeBridge rather than the strongest listed baseline | financial forecasting · CSI 500 | ARR: 0.214 -> 0.285 | Helped |
| Remove non-stationarity in Integrated Attention while retaining it in Cointegrated Attention (ablation) | TimeBridge · Weather | MSE: 0.220 -> 0.219 | Helped |
| Retain non-stationarity in both attention modules (ablation) | TimeBridge · Weather | MSE: 0.219 -> 0.220 | Hurt |
| Remove non-stationarity from Cointegrated Attention as well (ablation) | TimeBridge · Weather | MSE: 0.219 -> 0.219 | No clear effect |
| Include both Integrated and Cointegrated Attention in that order (ablation) | TimeBridge · Weather | MSE: 0.222 -> 0.219 | Helped |
| Remove Cointegrated Attention (ablation) | TimeBridge · Weather | MSE: 0.219 -> 0.220 | Hurt |
| Remove Integrated Attention (ablation) | TimeBridge · Weather | MSE: 0.219 -> 0.222 | Hurt |
| Reverse the order of the attention modules and replace downsampling with upsampling (ablation) | TimeBridge · Weather | MSE: 0.219 -> 0.227 | Hurt |
| Use channel-independent modeling in both attention modules instead of channel-dependent Cointegrated Attention (ablation) | TimeBridge · Weather | MSE: 0.219 -> 0.218 | No clear effect |
Surprising findings
- Modeling short-term inter-variate relationships causes severe spurious regression, and CI is better than CD on low-channel datasets like Weather while CD is better on Traffic.
- Ordering Cointegrated Attention before Integrated Attention performs worst, possibly losing short-term features.
Limitations
- Only uses Cointegrated Attention for datasets with many channels; ETT datasets use Integrated Attention only, a design choice based on dataset properties.
- Theoretical propositions rely on Brownian-motion idealizations and may not hold for real data.
Experimental setup
Datasets: ETTm1 ETTm2 ETTh1 ETTh2 Weather Electricity Traffic Solar-Energy PeMS03 PeMS04 PeMS07 PeMS08
Benchmarks: ETTm1 ETTm2 ETTh1 ETTh2 Weather Electricity Traffic Solar-Energy PeMS03 PeMS04 PeMS07 PeMS08
Metrics: MSE MAE MAPE RMSE ARR AVol MDD ASR CR IR
Baselines: DeformableTST ModernTCN TimeMixer iTransformer PatchTST Crossformer Leddam MICN TimesNet DLinear SCINet DUET
Builds on: PatchTST iTransformer RevIN
Closest papers by meaning
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- Unlocking the Power of Patch: Patch-Based MLP for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.84)
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