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Rethinking Channel Dependence for Multivariate Time Series Forecasting: Learning from Leading Indicators
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Proposes LIFT, a plug-in that dynamically estimates leading indicators and leading steps via FFT-based cross-correlation and refines backbone forecasts with an adaptive frequency mixer, plus a lightweight linear model LightMTS.
Problem
Channel-independent forecasters ignore cross-variate dependence, while channel-dependent models overfit because lead-lag relationships between variates change over time.
Approach
Model locally stationary lead-lag relationships: estimate, per time step, each variate's leading indicators and leading steps via FFT cross-correlation, shift leaders to align with the target horizon, and refine backbone predictions in the frequency domain with state-dependent adaptive filters.
Key results
- LIFT improves its backbones by 5.4% on average across six datasets in the main table (7.9% over CI models, 3.0% over CD models).
- On Solar, LIFT with CD backbone MTGNN reaches MSE 0.069 at horizon 24 versus 0.070 for MTGNN alone and 0.095 for PatchTST; LIFT gains up to 12.3% on PeMSD8 at horizon 720.
- LightMTS, a linear CI backbone with LIFT-style refinement, surpasses PatchTST by 3.2% on Weather and 0.7% on Electricity per the paper.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add LIFT to CI backbones | PatchTST and DLinear · Six MTS datasets | forecasting error: 7.9% | Helped |
| Add LIFT to CD backbones | Crossformer and MTGNN · Six MTS datasets | forecasting error: 3.0% | Helped |
| Add LIFT to PatchTST | PatchTST · ETTh1, H=336 | MSE: 0.431 -> 0.433 | Hurt |
| Add LIFT to DLinear | DLinear · ETTh1, H=720 | MSE: 0.472 -> 0.509 | Hurt |
| Add the leading-indicator influence term (ablation) | LightMTS · Weather, Electricity, and Traffic, H=96 | relative MSE | Helped |
| Add the leading-indicator difference term (ablation) | LightMTS · Weather, Electricity, and Traffic, H=96 | relative MSE | Helped |
| Adaptively filter frequency components (ablation) | LightMTS · Weather, Electricity, and Traffic, H=96 | relative MSE | Helped |
| Increase the number of selected leading indicators K (ablation) | DLinear + LIFT · Most datasets, H=96 | MSE | Mixed |
| Increase the number of variate states N (ablation) | DLinear + LIFT · Most datasets, H=96 | MSE | Helped |
| Model variate states rather than ignore them (ablation) | DLinear + LIFT · Weather, H=96 | MSE | Helped |
Surprising findings
- LIFT fails in some cases on ETTh1, ETTm1 and ILI, which the authors attribute to only 7 variates providing few leading indicators.
- The lead-lag relationships and leading steps change substantially from training to test data, which the authors argue is why static CD models overfit.
Limitations
- Gains are small or negative on datasets with few variates (ETTh1, ETTm1, ILI with 7 variates).
- Relies on a strong backbone for Traffic; LightMTS trails PatchTST there.
- Leading step estimation is approximate and the authors leave refinement of leading step estimation to future work.
Experimental setup
Datasets: Weather Electricity Traffic Solar Wind PeMSD8 ETTh1 ETTm1 ILI
Benchmarks: Weather Electricity Traffic Solar Wind PeMSD8 ETTh1 ETTm1 ILI
Metrics: MSE MAE MACs parameter count GPU memory inference time
Baselines: PatchTST DLinear Crossformer MTGNN FEDformer Autoformer Informer
Builds on: PatchTST DLinear Crossformer MTGNN RevIN
Closest papers by meaning
- From Similarity to Superiority: Channel Clustering for Time Series Forecasting (NeurIPS 2024 · similarity 0.89)
- Revitalizing Multivariate Time Series Forecasting: Learnable Decomposition with Inter-Series Dependencies and Intra-Series Variations Modeling (ICML 2024 · similarity 0.87)
- Unlocking the Power of Patch: Patch-Based MLP for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.87)
- SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion (NeurIPS 2024 · similarity 0.87)
- A Closer Look at Transformers for Time Series Forecasting: Understanding Why They Work and Where They Struggle (ICML 2025 · similarity 0.86)
- Multivariate Time Series Forecasting needs Cross Variable Loss (NeurIPS 2026 · similarity 0.86)
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