Research map / Time series / Long-term forecasting
xPatch: Dual-Stream Time Series Forecasting with Exponential Seasonal-Trend Decomposition
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Proposes xPatch, a dual-stream non-transformer forecaster using EMA seasonal-trend decomposition, an MLP linear stream plus a CNN patch-based non-linear stream, an arctangent loss, and a sigmoid learning-rate schedule.
Problem
Long-term time series forecasting: transformers' permutation-invariant attention may fail to exploit temporal order, and existing moving-average decomposition introduces padding bias and loses trend features.
Approach
Replace moving-average decomposition with exponential moving average (EMA) decomposition, process trend and seasonal parts in a dual flow (MLP linear stream for trend, CNN with patching and channel-independence for seasonality), and train with an arctangent-scaled MAE loss and a sigmoid learning-rate schedule.
Key results
- Under unified settings (L=96, ILI L=36), xPatch achieves best average MSE on 60% of datasets and best MAE on 70%; vs CARD it improves MSE by 2.46% and MAE by 2.34%.
- With hyperparameter search, xPatch improves over CARD by 5.29% MSE and 3.81% MAE, and over PatchTST by 7.87% MSE and 8.59% MAE.
- Adding EMA decomposition to PatchTST, DLinear, FEDformer and Autoformer reduces their errors in the reported ablation (e.g., 1.91% MSE gain for PatchTST on ILI-averaged gains reported in table).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use xPatch instead of CARD | Long-term forecasting benchmarks, unified settings · Nine datasets | MSE: 2.46% | Helped |
| Use xPatch instead of CARD | Long-term forecasting benchmarks, unified settings · Nine datasets | MAE: 2.34% | Helped |
| Use xPatch instead of PatchTST | Long-term forecasting benchmarks, unified settings · Nine datasets | MSE: 4.76% | Helped |
| Use xPatch instead of PatchTST | Long-term forecasting benchmarks, unified settings · Nine datasets | MAE: 6.20% | Helped |
| Replace the original decomposition with EMA (alpha 0.3) (ablation) | DLinear · Nine forecasting datasets | MSE: 2.93% | Helped |
| Replace the original decomposition with EMA (alpha 0.3) (ablation) | DLinear · Nine forecasting datasets | MAE: 3.00% | Helped |
| Replace the original decomposition with EMA (alpha 0.3) (ablation) | PatchTST · Nine forecasting datasets | MSE: 1.91% | Helped |
| Replace the original decomposition with EMA (alpha 0.3) (ablation) | PatchTST · Nine forecasting datasets | MAE: 1.25% | Helped |
| Set alpha to a learnable parameter rather than fixed (ablation) | xPatch · Forecasting benchmarks | forecasting performance | Helped |
| Use the original stream assignment: seasonality to nonlinear stream, trend to linear stream (ablation) | xPatch dual-flow network · Forecasting benchmarks | forecasting performance | Helped |
| Use alpha 0.3 rather than other tested fixed alpha values (ablation) | xPatch, DLinear, and PatchTST · Weather, Traffic, Electricity | MAE | Helped |
Surprising findings
- Exchange-rate results show xPatch is not best there; PatchTST and CARD are competitive, and xPatch is weaker on Traffic MSE than CARD and iTransformer.
Limitations
- Higher computational cost than single-stream CNN and MLP models (DLinear is faster).
- Does not win on every dataset (e.g., Exchange-rate and some Traffic metrics).
- Relies on fixed alpha=0.3 for EMA; learnable alpha gave marginal gains with large training-time cost.
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Weather Traffic Electricity Exchange-rate ILI Solar-energy
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Weather Traffic Electricity Exchange-rate Solar-energy ILI
Metrics: MSE MAE
Baselines: CARD TimeMixer iTransformer RLinear PatchTST MICN DLinear TimesNet ETSformer Autoformer FEDformer
Builds on: PatchTST CARD DLinear Autoformer RevIN
Closest papers by meaning
- DeformableTST: Transformer for Time Series Forecasting without Over-reliance on Patching (NeurIPS 2024 · similarity 0.86)
- TimePerceiver: An Encoder-Decoder Framework for Generalized Time-Series Forecasting (NeurIPS 2025 · similarity 0.86)
- Unlocking the Power of Patch: Patch-Based MLP for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.86)
- TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables (NeurIPS 2024 · similarity 0.86)
- Towards a General Time Series Forecasting Model with Unified Representation and Adaptive Transfer (ICML 2025 · similarity 0.85)
- OLinear: A Linear Model for Time Series Forecasting in Orthogonally Transformed Domain (NeurIPS 2025 · similarity 0.85)
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