Modeling Temporal Symmetry: Dual-Component Framework for Trends and Fluctuations in Time Series Forecasting
Wei Ran, Kanlun Tan, Zhouyuan Zhang, Jiatian Pi, Yichuan Zhang · Symmetry · 2025
Time-series forecasting is a cornerstone of decision making in domains such as finance, energy management, and meteorology, where precise predictions drive both economic and operational efficiency. However, traditional time-domain methods often struggle to capture the intricate symmetries and hierarchical dependencies inherent in complex multivariate time-series data. These methods frequently fail to distinguish between global trends and localized fluctuations, limiting their ability to model the multifaceted temporal dynamics that arise across different time scales. To address these challenges, we propose a novel dual-component framework that explicitly leverages the symmetry between long-term trends and short-term fluctuations. Inspired by the principles of signal decomposition, we partition time-series data into a low-frequency stabilization component and a high-frequency fluctuation component. The stabilization component captures inter-variable relationships and global frequency-domain component dependencies through Fourier-transformed frequency-domain representations, variable-oriented attention mechanisms, and dilated causal convolutions. Meanwhile, the fluctuation component models localized dynamics using a multi-granularity structure and time-step attention mechanisms to enhance the sensitivity and robustness to transient variations. By integrating these complementary perspectives, our approach provides a more holistic representation of time-series dynamics. Comprehensive experiments on benchmark datasets from electricity, transportation, and weather domains demonstrate that our method consistently outperforms state-of-the-art models, achieving superior accuracy. Beyond predictive performance, our framework offers a deeper interpretability of temporal behaviors, highlighting its potential for practical applications in complex systems. This work underscores the importance of symmetry-aware modeling in advancing time-series forecasting methodologies.