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TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting
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Proposes TimeKAN, a lightweight KAN-based Decomposition-Learning-Mixing architecture that cascades frequency bands via FFT-based upsampling and learns each band with Multi-order Chebyshev KANs for long-term time series forecasting.
Problem
Long-term time series forecasting is hard because mixed frequency components have varying information density, and uniform modeling of each frequency band yields inaccurate representations.
Approach
Cascaded frequency decomposition via moving-average downsampling and FFT-based frequency upsampling yields per-band residuals, each modeled by a KAN whose Chebyshev polynomial order increases from low to high frequency; the Decomposition-Learning-Mixing block is repeated.
Key results
- TimeKAN achieves best average MSE/MAE on ETTh1 (0.417/0.427), ETTm1 (0.376/0.395), and Weather (0.242/0.272) among compared methods, with 22 first-place counts out of 48 metric-settings reported.
- On Electricity, iTransformer (0.178 MSE) beats TimeKAN (0.197 MSE) at the 96-input setting, with TimeKAN ranking behind TimeMixer there.
- TimeKAN uses 12.84K to 38.12K parameters across datasets; on Weather it needs about 20% of TimeMixer's parameters and 36% of its MACs.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use TimeKAN instead of iTransformer | ETTh1 forecasting · ETTh1 Avg | MSE: 0.454 -> 0.417 | Helped |
| Use TimeKAN instead of Time-FFM | ETTh2 forecasting · ETTh2 Avg | MSE: 0.382 -> 0.383 | Hurt |
| Use TimeKAN instead of TimeMixer | ETTm1 forecasting · ETTm1 Avg | MSE: 0.382 -> 0.376 | Helped |
| Use TimeKAN instead of TimeMixer | ETTm2 forecasting · ETTm2 Avg | MSE: 0.277 -> 0.277 | No clear effect |
| Use TimeKAN instead of TimeMixer | Weather forecasting · Weather Avg | MSE: 0.245 -> 0.242 | Helped |
| Use TimeKAN instead of iTransformer | Electricity forecasting · Electricity Avg | MSE: 0.178 -> 0.197 | Hurt |
| Use Frequency Upsampling rather than Linear Mapping (ablation) | TimeKAN · ETTh1 | MSE: 0.401 -> 0.367 | Helped |
| Use Frequency Upsampling rather than Linear Interpolation (ablation) | TimeKAN · ETTh1 | MSE: 0.383 -> 0.367 | Helped |
| Use Frequency Upsampling rather than Transposed Convolution (ablation) | TimeKAN · ETTh1 | MSE: 0.377 -> 0.367 | Helped |
| Use Multi-order KANs instead of MLPs (ablation) | TimeKAN · ETTh1 | MSE: 0.376 -> 0.367 | Helped |
| Use Multi-order KANs instead of fixed order-2 KANs (ablation) | TimeKAN · ETTh1 | MSE: 0.376 -> 0.367 | Helped |
| Use Multi-order KANs instead of fixed order-5 KANs (ablation) | TimeKAN · ETTh1 | MSE: 0.380 -> 0.367 | Helped |
Surprising findings
- TimeKAN underperforms on Electricity at look-back 96 (MSE 0.197 vs iTransformer 0.178), but with look-back 512 it reaches the best Electricity results in the appendix.
Limitations
- Weaker on Electricity with the 96-step look-back window, where iTransformer and TimeMixer are better.
- Frequency band count (3-4 best) is a hyperparameter selected empirically.
Experimental setup
Datasets: Weather ETTh1 ETTh2 ETTm1 ETTm2 Electricity
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Weather Electricity
Metrics: MSE MAE Params MACs
Baselines: TimeMixer iTransformer Time-FFM PatchTST TimesNet MICN DLinear FreTS FiLM FEDformer Autoformer
Builds on: ChebyshevKAN Kolmogorov-Arnold Network DLinear TimeMixer
Closest papers by meaning
- FilterNet: Harnessing Frequency Filters for Time Series Forecasting (NeurIPS 2024 · similarity 0.88)
- Towards a General Time Series Forecasting Model with Unified Representation and Adaptive Transfer (ICML 2025 · similarity 0.87)
- Rethinking Fourier Transform from A Basis Functions Perspective for Long-term Time Series Forecasting (NeurIPS 2024 · similarity 0.86)
- TimeEmb: A Lightweight Static-Dynamic Disentanglement Framework for Time Series Forecasting (NeurIPS 2025 · similarity 0.86)
- CFPT: Empowering Time Series Forecasting through Cross-Frequency Interaction and Periodic-Aware Timestamp Modeling (ICML 2025 · similarity 0.86)
- Adaptive Multi-Scale Decomposition Framework for Time Series Forecasting (AAAI 2025 · similarity 0.85)
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