TF4TF: Multi-semantic modeling within the time–frequency domain for long-term time-series forecasting

Long-term Time Series Forecasting (LTSF) plays a crucial role in real-world applications for early warning and decision-making. Time series inherently embody complex semantic information, including segment semantics, global–local semantics, and multi-view semantics, the thorough mining of which can significantly enhance the accuracy. Previous works have not been able to simultaneously address all of the semantic information mentioned above. Meanwhile, the thorough mining of semantic information introduces additional computational complexity, resulting in inefficiency issues for existing multi-semantic information mining methods. Considering the aforementioned situation, we propose a multi-semantic method within the Time–Frequency domain For long-term Time-series Forecasting (TF4TF), which can balance complex semantic information mining and efficiency. For sequences with segment semantics following patching process, mining is conducted from both time and frequency domain perspectives to extract Multi-View Semantics. Within this framework, Progressive Local Windows (PLW) blocks and Global Frequency Filtering (GFF) blocks are specifically designed, which achieve efficient mining of multi-scale information while maintaining lower complexity. Ultimately, forecasting is achieved by integrating the semantic information outlined above. Our proposed method, TF4TF, has achieved state-of-the-art (SOTA) results on seven real-world time series forecasting datasets. © 2024 Elsevier B.V.