mlsanityData to 7 Oct 2026

PHAT: Modeling Period Heterogeneity for Multivariate Time Series Forecasting

arXiv 2602.00654 ↗First posted 31 Jan 2026cs.LGcited by 2

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Abstract (arXiv)

While existing multivariate time series forecasting models have advanced significantly in modeling periodicity, they largely neglect the periodic heterogeneity common in real-world data, where variables exhibit distinct and dynamically changing periods. To effectively capture this periodic heterogeneity, we propose PHAT (Period Heterogeneity-Aware Transformer). Specifically, PHAT arranges multivariate inputs into a three-dimensional "periodic bucket" tensor, where the dimensions correspond to variable group characteristics with similar periodicity, time steps aligned by phase, and offsets within the period. By restricting interactions within buckets and masking cross-bucket connections, PHAT effectively avoids interference from inconsistent periods. We also propose a positive-negative attention mechanism, which captures periodic dependencies from two perspectives: periodic alignment and periodic deviation. Additionally, the periodic alignment attention scores are decomposed into positive and negative components, with a modulation term encoding periodic priors. This modulation constrains the attention mechanism to more faithfully reflect the underlying periodic trends. A mathematical explanation is provided to support this property. We evaluate PHAT comprehensively on 14 real-world datasets against 18 baselines, and the results show that it significantly outperforms existing methods, achieving highly competitive forecasting performance. Our sources is available at GitHub.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 49 of its 84 references that are in the map. First posted on arXiv 31 Jan 2026.

Builds on

49 of 84 references.

References · 49

  1. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,141
  2. 2022A Time Series is Worth 64 Words: Long-term Forecasting with Transformerscited by 1,981
  3. 2021Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecastingcited by 1,654
  4. 2022Are Transformers Effective for Time Series Forecasting?cited by 1,400
  5. 2022FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecastingcited by 1,200
  6. 2022TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysiscited by 1,030
  7. 2023iTransformer: Inverted Transformers Are Effective for Time Series Forecastingcited by 906
  8. 2019Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecastingcited by 606
  9. 2020Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networkscited by 563
  10. 2022Transformers in Time Series: A Surveycited by 489
  11. 2022Non-stationary Transformers: Exploring the Stationarity in Time Series Forecastingcited by 385
  12. 2024TimeMixer: Decomposable Multiscale Mixing for Time Series Forecastingcited by 333
37 more
  1. 2024TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methodscited by 242
  2. 2024Foundation Models for Time Series Analysis: A Tutorial and Surveycited by 234
  3. 2023FITS: Modeling Time Series with 10k Parameterscited by 185
  4. 2022FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecastingcited by 147
  5. 2024TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysiscited by 113
  6. 2024DUET: Dual Clustering Enhanced Multivariate Time Series Forecastingcited by 104
  7. 2024SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameterscited by 103
  8. 2024Pathformer: Multi-scale Transformers with Adaptive Pathways for Time Series Forecastingcited by 102
  9. 2024CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patternscited by 102
  10. 2024CATCH: Channel-Aware multivariate Time Series Anomaly Detection via Frequency Patchingcited by 91
  11. 2024FreDF: Learning to Forecast in the Frequency Domaincited by 77
  12. 2025Transformers without Normalizationcited by 69
  13. 2025TimeFilter: Patch-Specific Spatial-Temporal Graph Filtration for Time Series Forecastingcited by 60
  14. 2022Triformer: Triangular, Variable-Specific Attentions for Long Sequence Multivariate Time Series Forecasting--Full Versioncited by 59
  15. 2025TAB: Unified Benchmarking of Time Series Anomaly Detection Methodscited by 58
  16. 2025Rethinking Irregular Time Series Forecasting: A Simple yet Effective Baselinecited by 54
  17. 2025DBLoss: Decomposition-based Loss Function for Time Series Forecastingcited by 44
  18. 2024Fredformer: Frequency Debiased Transformer for Time Series Forecastingcited by 43
  19. 2024xPatch: Dual-Stream Time Series Forecasting with Exponential Seasonal-Trend Decompositioncited by 35
  20. 2024Adaptive Multi-Scale Decomposition Framework for Time Series Forecastingcited by 34
  21. 2025Enhancing Time Series Forecasting through Selective Representation Spaces: A Patch Perspectivecited by 34
  22. 2025DAG: A Dual Correlation Network for Time Series Forecasting with Exogenous Variablescited by 30
  23. 2025Aurora: Towards Universal Generative Multimodal Time Series Forecastingcited by 28
  24. 2025TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecastingcited by 27
  25. 2025OLinear: A Linear Model for Time Series Forecasting in Orthogonally Transformed Domaincited by 25
  26. 2025Amplifier: Bringing Attention to Neglected Low-Energy Components in Time Series Forecastingcited by 23
  27. 2025FinTSB: A Comprehensive and Practical Benchmark for Financial Time Series Forecastingcited by 23
  28. 2025Time-o1: Time-Series Forecasting Needs Transformed Label Alignmentcited by 22
  29. 2025Bridging Past and Future: Distribution-Aware Alignment for Time Series Forecastingcited by 19
  30. 2025DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignmentcited by 13
  31. 2025FreqMoE: Enhancing Time Series Forecasting through Frequency Decomposition Mixture of Expertscited by 11
  32. 2024ATFNet: Adaptive Time-Frequency Ensembled Network for Long-term Time Series Forecastingcited by 8
  33. 2024Test Time Learning for Time Series Forecastingcited by 5
  34. 2025DeepFilter: A Transformer-style Framework for Accurate and Efficient Process Monitoringcited by 5
  35. 2025Spatiotemporal Causal Decoupling Model for Air Quality Forecastingcited by 3
  36. 2026To See Far, Look Close: Evolutionary Forecasting for Long-term Time Seriescited by 1
  37. 2026A General ReLearner: Empowering Spatiotemporal Prediction by Re-learning Input-label Residualcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026GCGNet: Graph-Consistent Generative Network for Time Series Forecasting with Exogenous Variablescited by 11
  2. 2026SemPSG: A Semantic Channel-Aware Foundation Model for Polysomnography Analysiscited by 0