Long-term time series forecasting has been widely studied, yet two aspects remain insufficiently explored: the interaction learning between different frequency components and the exploitation of periodic characteristics inherent in timestamps. To address the above issues, we propose CFPT, a novel method that empowering time series forecasting through Cross-Frequency Interaction (CFI) and Periodic-Aware Timestamp Modeling (PTM). To learn cross-frequency interactions, we design the CFI branch to process signals in frequency domain and captures their interactions through a feature fusion mechanism. Furthermore, to enhance prediction performance by leveraging timestamp periodicity, we develop the PTM branch which transforms timestamp sequences into 2D periodic tensors and utilizes 2D convolution to capture both intra-period dependencies and inter-period correlations of time series based on timestamp patterns. Extensive experiments on multiple real-world benchmarks demonstrate that CFPT achieves state-of-the-art performance in long-term forecasting tasks. The code is publicly available at this repository: https://github.com/BUPT-SN/CFPT.

Long-term time series forecasting has been widely studied for applications spanning numerous sectors, including energy consumption, transportation, and financial markets. However, two aspects remain insufficiently explored: the interaction learning between different frequency components and the exploitation of periodic characteristics inherent in timestamps.We propose CFPT, a novel framework that empowers time series forecasting through two specialized branches. The Cross-Frequency Interaction (CFI) branch processes signals in the frequency domain and captures interactions between low-frequency components carrying fundamental patterns and high-frequency components reflecting short-term dynamics. Meanwhile, our Periodic-Aware Timestamp Modeling (PTM) branch transforms timestamp sequences into 2D periodic tensors, utilizing 2D convolution to capture both intra-period dependencies and inter-period correlations based on timestamp patterns.Our extensive experiments on multiple real-world benchmarks demonstrate that CFPT achieves state-of-the-art performance in long-term forecasting tasks. This advancement enhances prediction accuracy and provides deeper insights into temporal data patterns, helping to improve decision-making processes across diverse domains.