FAITH: Frequency-domain Attention In Two Horizons for time series forecasting

Time Series Forecasting (TSF) plays a crucial role in various sectors, including industrial maintenance, weather prediction, energy management, traffic control, and financial planning. Current deep learning-based predictive models often exhibit significant deviations between their forecasting outcomes and the ground truth because they lack an efficient method to extract both the global frequency-domain information of each variable and the relationships between different variables. To tackle this challenge, we introduce an innovative model- Frequency-domain Attention In Two Horizons (FAITH). FAITH decomposes time series into trend and seasonal components using a multi-scale adaptive decomposition and fusion architecture and processes them separately. It utilizes two modules - the Frequency Channel Feature Extraction Module (FCEM) and the Frequency Temporal Feature Extraction Module (FTEM) - to capture inter-channel relationships at a finer granularity and to extract global temporal information from the frequency domain of different variables. This significantly enhances its ability to handle long-term dependencies and complex patterns. Furthermore, FAITH achieves theoretically linear complexity by modifying the time-frequency domain transformation method, effectively reducing computational costs. Extensive experiments across six benchmarks for long-term forecasting and five benchmarks for short-term forecasting demonstrate that FAITH outperforms existing models in various domains, such as electricity, weather, and traffic. These results validate the effectiveness and superiority of FAITH in both long-term and short-term time series forecasting tasks. Our codes and data are available at https://github.com/LRQ577/FAITH