MoFo: Empowering Long-term Time Series Forecasting with Periodic Pattern Modeling
Jiaming Ma, Binwu Wang, Qihe Huang, Guanjun Wang, Pengkun Wang, Zhengyang Zhou, Yang Wang
The stable periodic patterns present in time series data serve as the foundation for long-term forecasting. However, existing models suffer from limitations such as continuous and chaotic input partitioning, as well as weak inductive biases, which restrict their ability to capture such recurring structures. In this paper, we propose MoFo, which interprets periodicity as both the correlation of period-aligned time steps and the trend of period-offset time steps. We first design period-structured patches—2D tensors generated through discrete sampling—where each row contains only period-aligned time steps, enabling direct modeling of periodic correlations. Period-offset time steps within a cycle are aligned in columns. To capture trends across these offset time steps, we introduce a period-aware modulator. This modulator introduces an adaptive strong inductive bias through a regulated relaxation function, encouraging the model to generate attention coefficients that align with periodic trends. This function is end-to-end trainable, enabling the model to adaptively capture the distinct periodic patterns across diverse datasets. Extensive empirical results on popular benchmark datasets demonstrate that MoFo achieves competitive performance compared to 17 advanced baselines, while offering up to 14x memory efficiency gain and 10x faster training speed.