Research map / Time series / Long-term forecasting
FreDF: Learning to Forecast in the Frequency Domain
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Proposes FreDF, which adds an L1 loss on FFT-transformed forecasts and labels to the direct forecast objective to reduce bias from label autocorrelation in time series forecasting.
Problem
Direct forecast (DF) training for multi-step time series forecasting assumes conditional independence among future labels, ignoring label autocorrelation, which biases the learning objective.
Approach
Align forecasts and labels in the frequency domain via FFT, where frequency components are approximately decorrelated, and combine an L1 frequency loss with the temporal MSE loss, keeping DF's single-pass multi-output inference.
Key results
- On ETTm1, FreDF lowers iTransformer's MSE by 0.019 (0.415 to 0.392 averaged over horizons) and achieves best MSE on 6 of 9 long-term datasets (e.g., ETTm1 0.392, ETTh1 0.437, ECL 0.170).
- FreDF-T, FreDF-D and FreDF-2 variants reduce iTransformer ETTh1 MSE by 2.63%, 0.92% and 3.94% respectively.
- With only 30% of training data, frequency-domain learning reportedly matches time-domain learning with full data on ETTm1.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add frequency-domain loss to iTransformer | iTransformer · Long-term forecasting; most reported datasets, including ETTm1 | MSE: 0.415 -> 0.392 | Helped |
| Add frequency loss instead of using temporal loss only (ablation) | iTransformer · ETTm1, ETTh1, ECL, Weather | MSE: 0.414 -> 0.392; 0.449 -> 0.437; 0.175 -> 0.169; 0.280 -> 0.257 | Helped |
| Add temporal loss to frequency-only FreDF (ablation) | iTransformer · ETTm1, ETTh1, ECL, Weather | MSE: 0.392 -> 0.391; 0.437 -> 0.437; 0.169 -> 0.169; 0.257 -> 0.253 | Mixed |
| Apply 2D FFT across time and variables rather than time-axis FFT (ablation) | FreDF with iTransformer · ETTh1 | MSE: 0.437 -> 0.432 | Helped |
| Use frequency-domain forecasting with 30% of training data rather than time-domain forecasting with the full training set | iTransformer · ETTm1 | forecast error | No clear effect |
Surprising findings
- Frequency-domain loss alone performs nearly as well as combined time+frequency loss, so the time-domain term adds only marginal gains in most cases.
- Autoformer with FreDF outperforms DLinear on ECL, despite Autoformer being older.
Limitations
- Relies on predefined Fourier bases that cannot adapt to specific data properties.
- Evaluated only on time series forecasting and imputation; generalization to other structured-label tasks (point clouds, speech, images) is untested.
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 ECL Traffic Weather PEMS03 PEMS08 M4
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 ECL Traffic Weather PEMS03 PEMS08 M4
Metrics: MSE MAE
Baselines: iTransformer FreTS TimesNet MICN TiDE DLinear FEDformer Autoformer Transformer TCN
Builds on: direct forecast FEDformer FreTS iTransformer DLinear
Closest papers by meaning
- Time-o1: Time-Series Forecasting Needs Transformed Label Alignment (NeurIPS 2025 · similarity 0.87)
- Towards a General Time Series Forecasting Model with Unified Representation and Adaptive Transfer (ICML 2025 · similarity 0.87)
- Learning Pattern-Specific Experts for Time Series Forecasting Under Patch-level Distribution Shift (NeurIPS 2025 · similarity 0.86)
- Not All Data are Good Labels: On the Self-supervised Labeling for Time Series Forecasting (NeurIPS 2025 · similarity 0.85)
- ARM: Refining Multivariate Forecasting with Adaptive Temporal-Contextual Learning (ICLR 2024 · similarity 0.84)
- Introducing Spectral Attention for Long-Range Dependency in Time Series Forecasting (NeurIPS 2024 · similarity 0.84)
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