Research map / Time series / Long-term forecasting
Frequency Adaptive Normalization For Non-stationary Time Series Forecasting
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes Frequency Adaptive Normalization (FAN), a model-agnostic reversible normalization that removes instance-wise top-K Fourier components from inputs and uses an MLP to predict their future evolution for denormalization.
Problem
Non-stationary time series forecasting where trend and evolving seasonal patterns shift between inputs and outputs; existing reversible instance normalization relies on mean/variance statistics that cannot capture seasonal patterns.
Approach
Instead of normalizing with temporal statistics, FAN filters the top-K amplitude Fourier components of each input instance (frequency residual learning) and trains a small MLP to predict the future values of those components, adding them back to the backbone's output.
Key results
- FAN applied to four backbones achieves 7.76%–37.90% average MSE improvements across eight benchmarks, per the abstract.
- With FEDformer backbone, FAN gives about 19.81% MSE improvement on average, despite FEDformer already using Fourier analysis.
- Averaged over all steps, FAN achieves best MSE on most datasets versus SAN, Dish-TS and RevIN (e.g., Exchange 0.149 vs 0.172 SAN with DLinear).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add FAN to DLinear | DLinear · Traffic, 96 | MSE: 0.504 -> 0.403 | Helped |
| Add FAN to DLinear | DLinear · Electricity, 96 | MSE: 0.195 -> 0.184 | Helped |
| Add FAN to DLinear | DLinear · Weather, 96 | MSE: 0.180 -> 0.173 | Helped |
| Add FAN to DLinear | DLinear · Exchange, 96 | MSE: 0.052 -> 0.053 | Hurt |
| Add FAN to DLinear | DLinear · ETTm2, 96 | MSE: 0.080 -> 0.078 | Helped |
| Add non-stationary pattern prediction (ablation) | FAN with SCINet · ETTh1, 96 | MSE: 0.582±0.001 -> 0.362±0.001 | Helped |
| Add FAN reconstruction (ablation) | FAN with SCINet · ETTh1, 96 | MSE: 0.549±0.071 -> 0.362±0.001 | Helped |
| Add the stationary forecasting backbone (ablation) | FAN · ETTh1, 96 | MSE: 0.392±0.001 -> 0.362±0.001 | Helped |
| Add non-stationary pattern prediction (ablation) | FAN with SCINet · Weather, 96 | MSE: 0.271±0.001 -> 0.170±0.001 | Helped |
| Add FAN reconstruction (ablation) | FAN with SCINet · Weather, 96 | MSE: 0.332±0.008 -> 0.170±0.001 | Helped |
| Add the stationary forecasting backbone (ablation) | FAN · Weather, 96 | MSE: 0.195±0.000 -> 0.170±0.001 | Helped |
| Add an extra MLP layer to the pattern prediction module (ablation) | FAN · ETTh1, 96 | MSE: 0.362±0.001 -> 0.362±0.001 | No clear effect |
Surprising findings
- Fixed global-frequency Fourier methods are shown to be inadequate because the principal frequencies vary across input instances.
Limitations
- K must be set by a heuristic (10% of maximum amplitude) rather than learned automatically.
- Gains are smaller on datasets with weak seasonality such as ETTh2, ExchangeRate and Weather.
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Electricity ExchangeRate Traffic Weather synthetic composite sinusoidal signals
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Electricity ExchangeRate Traffic Weather
Metrics: MSE MAE ADF test statistic
Baselines: DLinear FEDformer Informer SCINet SAN Dish-TS RevIN
Builds on: RevIN SAN Dish-TS channel independence
Closest papers by meaning
- PAMod: Modeling Cyclical Shifts via Phase-Amplitude Modulation for Non-stationary Time Series Forecasting (NeurIPS 2026 · similarity 0.87)
- TimeEmb: A Lightweight Static-Dynamic Disentanglement Framework for Time Series Forecasting (NeurIPS 2025 · similarity 0.86)
- SIN: Selective and Interpretable Normalization for Long-Term Time Series Forecasting (ICML 2024 · similarity 0.85)
- SEMPO: Lightweight Foundation Models for Time Series Forecasting (NeurIPS 2025 · similarity 0.85)
- Improving Time Series Forecasting via Instance-aware Post-hoc Revision (NeurIPS 2025 · similarity 0.85)
- Towards a General Time Series Forecasting Model with Unified Representation and Adaptive Transfer (ICML 2025 · similarity 0.85)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.