On the Performance of Legendre State-Space Models in Short-Term Time Series Forecasting

State-space models (SSMs) are a class of fundamental models in control theory. SSMs are well-known for their concise mathematical representations and capability of capturing the evolving dynamics of systems. They have also proven useful in time series modeling. Recent studies suggest that SSMs are able to conceptually generalize to classic machine learning models (CNNs, RNNs and RNN-variants) as well as provide theoretical justification for the design of novel sequence models. In this work, we investigate one type of SSM, the Legendre Memory Unit (LMU) and LMU’s parallelized variant (LMUFFT), and propose a stacking strategy leveraging the LMUFFT backbone and a Deep Adaptive Input Normalization (DAIN) scheme. Model performance is evaluated using short-term time series forecasting tasks formulated from real-world data. The proposed structure outperforms the traditional machine learning models in efficiency and prediction capability. Our results also suggest that this family of state-space models has potential in the realm of machine learning research. By shedding light on the benefits of SSMs in short-term time series forecasting, we hope to pique the interest of machine learning researchers in the use of SSMs and inspire further investigation into novel model designs based on these models.