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SparseTSF: Modeling Long-term Time Series Forecasting with *1k* Parameters
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Proposes SparseTSF, a sub-1k-parameter long-term time series forecaster that downsamples series by the known period into cross-period subsequences and applies a shared linear layer to predict trends.
Problem
Long-term time series forecasting models are large (millions of parameters), limiting use under restricted computational resources; the goal is an extremely lightweight LTSF model that remains competitive.
Approach
Cross-Period Sparse Forecasting reshapes a periodic series into w downsampled subsequences (one per phase) and applies a single parameter-shared linear layer across them, after a sliding convolutional aggregation, so periodicity is decoupled and only trend is predicted with under 1k parameters.
Key results
- SparseTSF uses 0.92K parameters on Electricity (horizon 720) versus 10.5K for FITS and 485.3K for DLinear, with 12.71M MACs.
- SparseTSF averaged MSE of 0.394 on ETTh1 across horizons (vs 0.410 FITS, 0.412 DLinear, 0.413 PatchTST) with look-back 720.
- Applying the Sparse technique to a Transformer reduced ETTh1 MSE by 21.4% on average, and to a linear model by 4.7%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use SparseTSF instead of FITS | ETTh1 forecasting at horizon 720 · ETTh1, horizon 720 | MSE: 0.427 -> 0.417 | Helped |
| use SparseTSF instead of FITS | ETTh2 forecasting at horizon 720 · ETTh2, horizon 720 | MSE: 0.374 -> 0.370 | Helped |
| use SparseTSF instead of PatchTST | Electricity forecasting at horizon 720 · Electricity, horizon 720 | MSE: 0.197 -> 0.203 | Hurt |
| use SparseTSF instead of PatchTST | Traffic forecasting at horizon 720 · Traffic, horizon 720 | MSE: 0.432 -> 0.445 | Hurt |
| use SparseTSF instead of FITS | Electricity forecasting at horizon 720 · Electricity, horizon 720 | parameters: 10.5 K -> 0.92 K | Helped |
| add the Sparse technique (ablation) | Linear on ETTh1 · ETTh1, horizon 96 | MSE: 0.371 -> 0.359 | Helped |
| add the Sparse technique (ablation) | Linear on ETTh2 · ETTh2, horizon 96 | MSE: 0.257 -> 0.267 | Hurt |
| set period w to 6 instead of 24 (ablation) | SparseTSF on ETTh1 · ETTh1, horizon 96 | MSE: 0.359 -> 0.376 | Hurt |
| set period w to 12 instead of 24 (ablation) | SparseTSF on ETTh1 · ETTh1, horizon 96 | MSE: 0.359 -> 0.369 | Hurt |
| set period w to 48 instead of 24 (ablation) | SparseTSF on ETTh1 · ETTh1, horizon 96 | MSE: 0.359 -> 0.380 | Hurt |
| add instance normalization (ablation) | SparseTSF on ETTh1 · ETTh1, horizon 96 | MSE: 0.37 -> 0.359 | Helped |
| add instance normalization (ablation) | SparseTSF on ETTh2 · ETTh2 | MSE | Helped |
Surprising findings
- Sparse technique improves a vanilla Transformer by a large margin on ETTh1 (e.g., 0.697 to 0.406 MSE at horizon 96).
- After fixing a long-standing evaluation bug, SparseTSF's advantage over baselines on ETTh2 shrinks (e.g., 0.294 vs FITS 0.272 at horizon 96).
Limitations
- Performs poorly with ultra-long periods (>100), where downsampling makes connections overly sparse.
- Struggles with data mixing multiple periods, since only one main period is decoupled.
- Requires a known or manually chosen periodicity w; not suited to data without clear periodicity such as financial data.
Experimental setup
Datasets: ETTh1 ETTh2 Electricity Traffic ETTm1 ETTm2 Weather
Benchmarks: ETTh1 ETTh2 Electricity Traffic ETTm1 ETTm2 Weather
Metrics: MSE MAE parameters MACs max memory epoch time
Baselines: Informer Autoformer Pyraformer FEDformer FiLM TimesNet PatchTST DLinear FITS
Builds on: DLinear FITS PatchTST N-HiTS OneShotSTL
Closest papers by meaning
- TimeBase: The Power of Minimalism in Efficient Long-term Time Series Forecasting (ICML 2025 · similarity 0.88)
- Parsimony or Capability? Decomposition Delivers Both in Long-term Time Series Forecasting (NeurIPS 2024 · similarity 0.88)
- Unlocking the Power of Patch: Patch-Based MLP for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.86)
- A Lightweight Sparse Interaction Network for Time Series Forecasting (AAAI 2025 · similarity 0.86)
- DeformableTST: Transformer for Time Series Forecasting without Over-reliance on Patching (NeurIPS 2024 · similarity 0.86)
- Time-LLM: Time Series Forecasting by Reprogramming Large Language Models (ICLR 2024 · similarity 0.85)
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