PHAT: Modeling Period Heterogeneity for Multivariate Time Series Forecasting

While existing multivariate time series forecasting models have advanced signif- icantly in modeling periodicity, they largely neglect the periodic heterogeneity common in real-world data, where variables exhibit distinct and dynamically chang- ing periods. To effectively capture this periodic heterogeneity, we propose PHAT (Period Heterogeneity-Aware Transformer). Specifically, PHAT arranges multivari- ate 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 inter- ference 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 expla- nation is provided to support this property. We evaluate PHAT comprehensively on 14 real-world datasets against 18 baselines, and the results show that it signif- icantly outperforms existing methods, achieving highly competitive forecasting performance. Our sources is available at Anonymous GitHub.