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Peri-midFormer: Periodic Pyramid Transformer for Time Series Analysis
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Proposes Peri-midFormer, which decomposes a time series into a top-down "Periodic Pyramid" of FFT-selected periodic components and applies periodic pyramid attention across levels for forecasting, imputation, classification and anomaly detection.
Problem
Time series analysis struggles to model complex, overlapping multi-periodic variations directly from 1D sequences; prior Transformers attend over scattered time points and ignore inclusion relationships between periods of different scales.
Approach
Decompose the seasonal part into FFT-selected periodic components arranged as a pyramid where longer periods contain shorter ones, and restrict self-attention to inclusion, same-level, and adjacent-level component relations (Periodic Pyramid Attention Mechanism), then aggregate multiple top-to-bottom "periodic feature flows" for reconstruction tasks.
Key results
- Long-term forecasting average MSE 0.308 / MAE 0.337, tying Time-LLM (0.308 / 0.334) on MSE and beating GPT4TS (0.324) and PatchTST (0.331).
- Classification average accuracy 76.6% across 10 UEA datasets, above TSLANet (76.0%) and GPT4TS (74.0%).
- Anomaly detection average F1 85.40%, second only to GPT4TS (86.72%); imputation average MSE 0.047 tied for best with GPT4TS.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use Peri-midFormer instead of TimesNet | Long-term forecasting on ETTh2 · ETTh2 | MSE: 0.408 -> 0.317 | Helped |
| use Peri-midFormer instead of Time-LLM | Long-term forecasting · 8 datasets average | MSE: 0.308 -> 0.308 | No clear effect |
| use Peri-midFormer instead of GPT4TS | Short-term forecasting · M4 | OWA: 0.861 -> 0.850 | Helped |
| use Peri-midFormer instead of TSLANet | Time series classification · UEA (10 subsets average) | accuracy: 76.0% -> 76.6% | Helped |
| use Peri-midFormer instead of GPT4TS | Imputation · 6 datasets average | MSE: 0.048 -> 0.047 | Helped |
| use Peri-midFormer instead of GPT4TS | Anomaly detection · 5 datasets average | F1-score: 86.72 -> 85.40 | Hurt |
| add periodic components rather than constructing the pyramid from patches (ablation) | Peri-midFormer · ETTh1 long-term forecasting | MSE: 0.734 -> 0.409 | Helped |
| add PPAM instead of periodic full attention (ablation) | Peri-midFormer · ETTh1 long-term forecasting | MSE: 0.581 -> 0.409 | Helped |
| add Periodic Feature Flows Aggregation (ablation) | Peri-midFormer · ETTh1 long-term forecasting | MSE: 0.433 -> 0.409 | Helped |
| add periodic components rather than constructing the pyramid from patches (ablation) | Peri-midFormer · ETTh2 long-term forecasting | MSE: 0.407 -> 0.317 | Helped |
| add PPAM instead of periodic full attention (ablation) | Peri-midFormer · ETTh2 long-term forecasting | MSE: 0.344 -> 0.317 | Helped |
| add Periodic Feature Flows Aggregation (ablation) | Peri-midFormer · ETTh2 long-term forecasting | MSE: 0.341 -> 0.317 | Helped |
Surprising findings
- Pre-interpolation (linear interpolation of missing values before the model) is needed to restore periodicity for imputation, and it improves other baselines too.
- Even without PPAM (periodic full attention), the periodic-component pipeline achieves competitive forecasting results, suggesting the periodic partitioning itself carries much of the gain.
Limitations
- Performance is weaker on datasets lacking clear periodicity (e.g., imputation on ETT, anomaly detection on binary event data).
- Requires tuning the number of pyramid levels k per task and dataset, with sensitivity to k.
- Imputation relies on pre-interpolation that is not a fully learned approach.
Experimental setup
Datasets: Weather Traffic Electricity Exchange ETTh1 ETTh2 ETTm1 ETTm2 M4 UEA (10 subsets) SMD MSL
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Weather Electricity Traffic Exchange M4 UEA classification (10 subsets) SMD MSL
Metrics: MSE MAE SMAPE MASE OWA accuracy F1-score
Baselines: TimesNet GPT4TS Time-LLM TSLANet iTransformer PatchTST DLinear FITS Pyraformer N-BEATS N-HiTS Anomaly Transformer
Builds on: TimesNet Pyraformer PatchTST Autoformer
Closest papers by meaning
- An Unsupervised Approach for Periodic Source Detection in Time Series (ICML 2024 · similarity 0.86)
- MPTSNet: Integrating Multiscale Periodic Local Patterns and Global Dependencies for Multivariate Time Series Classification (AAAI 2025 · similarity 0.85)
- TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis (ICLR 2025 · similarity 0.85)
- TSLANet: Rethinking Transformers for Time Series Representation Learning (ICML 2024 · similarity 0.84)
- CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns (NeurIPS 2024 · similarity 0.84)
- Detect, Explain, Interpret: An End-to-End Benchmark for Time Series Anomaly Detection, Explainability and Interpretability. (NeurIPS 2026 · similarity 0.83)
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