How to Train Your Mamba for Time Series Forecasting

State Space Models (SSMs) have emerged as a powerful framework for sequence modeling in recent years. By approximating continuous dynamical systems and applying discretization techniques, SSMs are particularly well-suited for modeling time-series data. However, despite their growing popularity, most existing applications of SSMs in time-series forecasting treat the models as black boxes. Besides, the underlying mechanisms that contribute to their effectiveness remain unclear, and common claims regarding their advantages in efficiency and expressiveness are not fully substantiated. To address these gaps, this paper establishes a theoretical connection between SSMs and classical spectral transformations from signal processing, thereby providing a more interpretable foundation. Furthermore, we conduct comprehensive ablation studies to examine the properties of different SSM configurations. Our goal is to offer both theoretical insight and empirical guidance for future research on SSM-based approaches in time-series forecasting.