HAR-former: Hybrid Transformer with an Adaptive Time-Frequency Representation Matrix for Long-Term Series Forecasting

Time series forecasting plays a critical role across various sectors, including economics, energy, transportation planning, and weather prediction. However, the inherent complexity and non-stationarity of real-world systems present considerable challenges for accurate modeling.Traditional approaches, often reliant on high-dimensional embeddings, tend to obscure multivariate relationships and suffer from performance limitations, particularly when dealing with intricate temporal patterns. To address these issues, we propose HAR-former, a Hybrid Transformer with an Adaptive Time-Frequency Representation Matrix ,which combines the strengths of Multi-Layer Perceptrons (MLPs) and Transformers to process trend and seasonal components, respectively. HAR-former leverages a novel adaptive time-frequency representation matrix to bridge the gap between time and frequency domains, allowing the model to capture both long-range dependencies and localized patterns. Extensive experimental evaluation on eight real-world benchmark datasets demonstrates that HAR-former significantly outperforms existing state-of-the-art (SOTA) methods, establishing it as a robust solution for complex time series forecasting tasks.