Research map / Time series / Long-term forecasting
CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns
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Proposes Residual Cycle Forecasting (RCF), which models global periodic patterns with learnable zero-initialized recurrent cycles and forecasts the residual, yielding CycleNet (Linear/MLP backbones) that reaches SOTA on long-term forecasting benchmarks with far fewer parameters.
Problem
Long-term time series forecasting (LTSF) relies on stable periodic patterns, but existing deep models capture them only implicitly from limited look-back windows; the paper asks whether periodicity can be modeled explicitly to improve accuracy and efficiency.
Approach
Learn globally shared recurrent cycles Q of length W (one per channel, initialized to zero) from the training set, subtract the aligned cyclic component from the input, forecast the residual with a simple backbone (Linear or MLP), and add the cycle back; RCF is also plug-and-play on existing models.
Key results
- CycleNet/MLP achieves the best average MSE on Electricity (0.168) and Solar-Energy (0.210) with look-back 96, and ranks first overall among compared models.
- Adding RCF to Linear, DLinear, PatchTST, and iTransformer improves Electricity MSE by roughly 5-28% (e.g., Linear 0.197 to 0.141 at horizon 96).
- CycleNet reduces parameters by over 90% versus iTransformer on Electricity (CycleNet/MLP 472.9K vs. 5.15M parameters, with no extra MACs from RCF).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add RCF to Linear (ablation) | Linear · Electricity, H=96 | MSE: 0.197 -> 0.141 | Helped |
| add RCF to MLP (ablation) | MLP · Traffic, H=96 | MSE: 0.500 -> 0.458 | Helped |
| add RCF to PatchTST (ablation) | PatchTST · Traffic | MSE: 0.436 -> 0.438 | Hurt |
| add RCF to PatchTST (ablation) | PatchTST · Traffic | MAE: 0.281 -> 0.264 | Helped |
| add RCF to iTransformer (ablation) | iTransformer · Traffic | MSE: 0.395 -> 0.415 | Hurt |
| add RCF to iTransformer (ablation) | iTransformer · Electricity | MSE: 0.148 -> 0.136 | Helped |
| use RCF instead of MOV decomposition (ablation) | Linear · Electricity | MSE: 0.167 -> 0.157 | Helped |
| set the cycle length to W=168 instead of W=144 (ablation) | CycleNet/Linear · Electricity, H=96 | MSE: 0.196 -> 0.142 | Helped |
| set the cycle length to W=144 instead of W=168 (ablation) | CycleNet/Linear · Solar-Energy, H=96 | MSE: 0.289 -> 0.208 | Helped |
| add instance normalization (ablation) | CycleNet · Solar-Energy | forecasting performance | Hurt |
| use CycleNet/MLP rather than CycleNet/Linear (ablation) | CycleNet · Electricity | MSE: 0.170 -> 0.168 | Helped |
| use CycleNet/MLP rather than CycleNet/Linear (ablation) | CycleNet · Traffic | MSE: 0.485 -> 0.472 | Helped |
Surprising findings
- Applying RCF to PatchTST and iTransformer lowers MAE but raises MSE on Traffic, attributed to outliers affecting the learned average cycles.
- Setting the cycle length W to a wrong value (e.g., 23 instead of 24) yields a flat learned pattern and performance nearly identical to no RCF.
Limitations
- Assumes a fixed, stable cycle length W; unsuitable for time-varying cycles (e.g., ECG) or channels with different cycle lengths.
- Sensitive to outliers because the learned cycle is a historical average; weaker on Traffic where inter-channel relations matter and iTransformer wins.
- Long-range cycles (e.g., yearly) need decades of training data, so the approach is limited to mid-range cycles.
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Electricity Solar-Energy Traffic Weather
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Electricity Solar-Energy Traffic Weather
Metrics: MSE MAE
Baselines: iTransformer PatchTST TimeMixer TimesNet DLinear FEDformer Autoformer Crossformer TiDE SCINet SparseTSF Leddam
Builds on: DLinear RevIN PatchTST iTransformer
Closest papers by meaning
- TimeBase: The Power of Minimalism in Efficient Long-term Time Series Forecasting (ICML 2025 · similarity 0.88)
- PGN: The RNN's New Successor is Effective for Long-Range Time Series Forecasting (NeurIPS 2024 · similarity 0.86)
- Unlocking the Power of Patch: Patch-Based MLP for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.86)
- Time-LLM: Time Series Forecasting by Reprogramming Large Language Models (ICLR 2024 · similarity 0.85)
- SparseTSF: Modeling Long-term Time Series Forecasting with *1k* Parameters (ICML 2024 · similarity 0.85)
- Unlocking the Power of LSTM for Long Term Time Series Forecasting (AAAI 2025 · similarity 0.85)
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