Research map / Time series / Long-term forecasting
TimeEmb: A Lightweight Static-Dynamic Disentanglement Framework for Time Series Forecasting
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Proposes TimeEmb, a lightweight time series forecaster that splits the rFFT spectrum into a learnable timestep-indexed embedding bank (time-invariant) and a learnable frequency filter on the residual (time-varying), reporting SOTA accuracy with far fewer parameters.
Problem
Temporal non-stationarity in time series forecasting: existing methods conflate long-term static patterns with short-term dynamic fluctuations, and strong disentanglement methods rely on rigid assumptions or are computationally heavy.
Approach
Decompose the frequency-domain representation into a time-invariant part retrieved from a learnable embedding bank indexed by the last timestep modulo M (a global, dataset-wide pattern), and a time-varying residual processed by a learnable complex frequency filter, then fuse, invert, and predict with a two-layer MLP.
Key results
- TimeEmb achieves best average MSE on ETTh1 (0.425), ETTh2 (0.362), ETTm1 (0.368) and Weather (0.237) at lookback 96 versus CycleNet and others.
- On Electricity at lookback 96, TimeEmb reports average MSE 0.167 and MAE 0.260, while using over 5x fewer parameters than iTransformer.
- Plugging the TimeEmb module into MLP backbones improves Electricity MSE by up to 22.6% (MLP, horizon 96) and Weather by up to 15.8% MAE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use TimeEmb instead of CycleNet | time-series forecaster · ETTh1 (avg, L=96) | MSE: 0.432 -> 0.425 | Helped |
| Use TimeEmb instead of Fredformer | time-series forecaster · ETTh2 (avg, L=96) | MSE: 0.365 -> 0.362 | Helped |
| Use TimeEmb instead of CycleNet | time-series forecaster · ETTm1 (avg, L=96) | MSE: 0.379 -> 0.368 | Helped |
| Use TimeEmb instead of CycleNet | time-series forecaster · ETTm2 (avg, L=96) | MSE: 0.266 -> 0.265 | Helped |
| Use TimeEmb instead of CycleNet | time-series forecaster · Weather (avg, L=96) | MSE: 0.243 -> 0.237 | Helped |
| Use TimeEmb instead of CycleNet | time-series forecaster · Electricity (avg, L=96) | MSE: 0.168 -> 0.167 | Helped |
| Use TimeEmb instead of iTransformer | time-series forecaster · Traffic (avg, L=96) | MSE: 0.428 -> 0.454 | Hurt |
| Integrate TimeEmb with MLP backbone | MLP · Electricity (L=96, H=96) | MSE: 0.177 -> 0.137; +22.6% | Helped |
| Integrate TimeEmb with Linear backbone | Linear · Weather (L=96, H=720) | MSE: 0.346 -> 0.349; -0.9% | Hurt |
| Replace the learned embedding bank with random initialization between training and testing (ablation) | TimeEmb · time-series forecasting (ablation; datasets not specified) | forecasting performance | Hurt |
| Fix the embedding bank to zeros or the global mean (ablation) | TimeEmb · time-series forecasting (ablation; datasets not specified) | forecasting performance | Hurt |
| Remove the time-invariant component X_s (ablation) | TimeEmb · time-series forecasting (ablation; datasets not specified) | forecasting performance | Hurt |
Surprising findings
- On Traffic at lookback 96, TimeEmb is worse than iTransformer and PatchTST in MSE, and Traffic results are not best across horizons.
- At lookback 720, CycleNet beats TimeEmb on several ETTh2 horizons and ETTm2 average MAE.
Limitations
- Traffic results lag some Transformer baselines (iTransformer, PatchTST) in several horizons.
- The embedding bank depends on a chosen period M (e.g., 24 or 7), and the paper relies on hyperparameter choices per dataset.
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Weather Electricity Traffic
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Weather Electricity Traffic
Metrics: MSE MAE
Baselines: CycleNet Fredformer FilterNet iTransformer PatchTST FITS FreTS DLinear SOFTS
Builds on: CycleNet DLinear FilterNet FITS
Closest papers by meaning
- TimeBase: The Power of Minimalism in Efficient Long-term Time Series Forecasting (ICML 2025 · similarity 0.90)
- OLinear: A Linear Model for Time Series Forecasting in Orthogonally Transformed Domain (NeurIPS 2025 · similarity 0.89)
- Learning Pattern-Specific Experts for Time Series Forecasting Under Patch-level Distribution Shift (NeurIPS 2025 · similarity 0.88)
- Revitalizing Multivariate Time Series Forecasting: Learnable Decomposition with Inter-Series Dependencies and Intra-Series Variations Modeling (ICML 2024 · similarity 0.88)
- TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting (ICLR 2024 · similarity 0.88)
- Enhancing Foundation Models for Time Series Forecasting via Wavelet-based Tokenization (ICML 2025 · similarity 0.88)
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