Affirm: Interactive Mamba with Adaptive Fourier Filters for Long-term Time Series Forecasting

In long-term series forecasting (LTSF), it is imperative for models to adeptly discern and distill from historical time series data to forecast future states. Although Transformerbased models excel at capturing long-term dependencies in LTSF, their practical use is limited by issues like computational inefficiency, noise sensitivity, and overfitting on smaller datasets. Therefore, we introduce a novel time series lightweight interactive Mamba with an adaptive Fourier filter model (Affirm). Specifically, (i) we propose an adaptive Fourier filter block. This neural operator employs Fourier analysis to refine feature representation, reduces noise with learnable adaptive thresholds, and captures inter-frequency interactions using global and local semantic adaptive Fourier filters via element-wise multiplication. (ii) A dual interactive Mamba block is introduced to facilitate efficient intra-modal interactions at different granularities, capturing more detailed local features and broad global contextual information, providing a more comprehensive representation for LTSF. Extensive experiments on multiple benchmarks demonstrate that Affirm consistently outperforms existing SOTA methods, offering a superior balance of accuracy and efficiency, making it ideal for various challenging scenarios with noise levels and data sizes. The codes and data are publicly available at https://github.com/zjuml/Affirm.