Research map / Time series / Long-term forecasting
CFPT: Empowering Time Series Forecasting through Cross-Frequency Interaction and Periodic-Aware Timestamp Modeling
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Proposes CFPT, a dual-branch long-term time series forecaster combining a cross-frequency interaction branch (coupled high/low-frequency feature modeling in the Fourier domain) with a periodic-aware timestamp branch that reshapes timestamp features into 2D period tensors for 2D convolution.
Problem
Long-term time series forecasting leaves under-explored both the interaction between different frequency components and the periodic structure encoded in timestamps.
Approach
Models interactions between low- and high-frequency DFT components through affine coupling layers (rather than independent processing or weighted sums), and models timestamp periodicity by slicing hierarchical timestamp features into period-length 2D tensors processed with 2D convolution, then fuses both branches by a fixed weighted sum.
Key results
- CFPT achieves best average MSE on 6 of 7 benchmarks in Table 1 (e.g., ETTm1 MSE 0.374 vs 0.382 for TimeXer), but not on Traffic (0.470 vs FilterNet 0.466 MSE... with iTransformer/FilterNet better).
- Ablation: removing the CFI branch raises ETTm1 MSE from 0.374 to 0.391 and Weather MSE from 0.240 to 0.251.
- Removing the PTM branch raises ETTm1 MSE from 0.374 to 0.385 and Weather MSE from 0.240 to 0.255.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use CFPT instead of TimeXer | long-term forecasting · ETTm1 | MSE: 0.382 -> 0.374 | Helped |
| use CFPT instead of TimeXer | long-term forecasting · ECL | MSE: 0.171 -> 0.164 | Helped |
| use CFPT instead of iTransformer | long-term forecasting · Traffic | MSE: 0.428 -> 0.470 | Hurt |
| add frequency decomposition of high- and low-frequency components (ablation) | CFPT · ETTm1 | MSE: 0.379 -> 0.374 | Helped |
| add cross-frequency coupling layers (ablation) | CFPT · ETTh2 | MSE: 0.394 -> 0.364 | Helped |
| add the CFI branch (ablation) | CFPT · ETTm1 | MSE: 0.391 -> 0.374 | Helped |
| use future timestamps instead of historical timestamps (ablation) | CFPT · Traffic (prediction length 720) | MSE: 0.544 vs 0.499 | Helped |
| use 2D timestamp modeling with periodic slicing instead of 1D convolution (ablation) | CFPT · ETTm1 | MSE: 0.376 -> 0.374 | Helped |
| add the PTM branch (ablation) | CFPT · ETTm1 | MSE: 0.385 -> 0.374 | Helped |
Limitations
- Periodic length P is fixed (set to 24) rather than adaptively detected, limiting use on irregular periodicity.
- Does not achieve best results on the Traffic dataset.
- Blending weight gamma is a constant hyperparameter rather than learned.
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 ECL Traffic Weather
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 ECL Traffic Weather
Metrics: MSE MAE
Baselines: TimeXer FilterNet iTransformer PatchTST FEDformer TimesNet DLinear RLinear
Builds on: TimesNet iTransformer FilterNet Informer Autoformer
Closest papers by meaning
- Affirm: Interactive Mamba with Adaptive Fourier Filters for Long-term Time Series Forecasting (AAAI 2025 · similarity 0.87)
- Rethinking Fourier Transform from A Basis Functions Perspective for Long-term Time Series Forecasting (NeurIPS 2024 · similarity 0.87)
- A Lightweight Sparse Interaction Network for Time Series Forecasting (AAAI 2025 · similarity 0.87)
- Unlocking the Power of Patch: Patch-Based MLP for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.86)
- xLSTM-Mixer: Multivariate Time Series Forecasting by Mixing via Scalar Memories (NeurIPS 2025 · similarity 0.86)
- TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting (ICLR 2024 · similarity 0.86)
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