Research map / Time series / Long-term forecasting
Times2D: Multi-Period Decomposition and Derivative Mapping for General Time Series Forecasting
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Times2D converts 1D time series into 2D tensors via FFT-identified periods and first/second derivative heatmaps, then uses 2D convolutions and attention to forecast, reporting state-of-the-art on M4 and long-term benchmarks.
Problem
Time series forecasting struggles with multi-periodicity, sharp fluctuations, and turning points when modeled as 1D sequences.
Approach
Reshape the series into 2D tensors per FFT-dominant period (periodic decomposition) and add first/second derivative heatmaps as a separate 2D branch, so 2D convolutions capture intra- and inter-period variation and sharp changes; outputs are summed for forecasting.
Key results
- On M4 yearly, Times2D achieves SMAPE 13.418 and OWA 0.787, slightly better than N-HITS (13.422 SMAPE).
- On long-term forecasting, Times2D reports average MSE 0.410 on ETTh1 and 0.250 on ETTm2 with best averages on most datasets, claiming about 5% average MSE reduction vs PatchTST and N-HITS.
- Times2D uses about 4329 MB RAM and 0.045 s/iter at horizon 384, with the efficiency comparison on a single NVIDIA L40S GPU.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace 1D temporal modeling with Times2D (2D periodic decomposition plus derivative heatmaps) | Times2D vs. 1D baselines · M4 yearly/quarterly/monthly and long-term benchmarks | SMAPE / MSE | Mixed |
| Times2D vs PatchTST on long-term averages | ETTh1, ETTh2, ETTm1, ETTm2, Weather · Long-term forecasting H=96-720 | MSE: small gains on most datasets, e.g. 0.410 vs 0.413 on ETTh1 | Helped |
| Times2D vs PatchTST on ETTh1 H=192 and H=720 horizons (MAE column) | ETTh1 · Long-term forecasting ETTh1 H=192 | MAE | Hurt |
Surprising findings
- On M4 quarterly, N-HITS (SMAPE 10.185) outperforms Times2D, and on Weather at horizon 96 the table reports lower MAE for CARD, suggesting the gains are not uniform.
Limitations
- Gains over strongest baselines are small and not uniform across M4 subsets and horizons
- Hyperparameter sensitivity analysis is limited to ETTh1 at horizon 96
- Paper itself notes model strengths and limitations are not examined in depth beyond aggregate metrics
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Weather Traffic M4
Benchmarks: M4 ETTh1 ETTh2 ETTm1 ETTm2 Weather
Metrics: MSE MAE SMAPE MASE OWA
Baselines: N-HITS PatchTST DLinear TimesNet MICN SCINet FEDformer Stationary FiLM LightTS Autoformer Informer
Builds on: TimesNet Autoformer FEDformer PatchTST
Closest papers by meaning
- Time-MMD: Multi-Domain Multimodal Dataset for Time Series Analysis (NeurIPS 2024 · similarity 0.86)
- TimeEmb: A Lightweight Static-Dynamic Disentanglement Framework for Time Series Forecasting (NeurIPS 2025 · similarity 0.86)
- TimeBase: The Power of Minimalism in Efficient Long-term Time Series Forecasting (ICML 2025 · similarity 0.85)
- Timer-XL: Long-Context Transformers for Unified Time Series Forecasting (ICLR 2025 · similarity 0.85)
- Towards a General Time Series Forecasting Model with Unified Representation and Adaptive Transfer (ICML 2025 · similarity 0.84)
- Learning Pattern-Specific Experts for Time Series Forecasting Under Patch-level Distribution Shift (NeurIPS 2025 · similarity 0.84)
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