Filter Banks: from Low-Rank Representations to Deep Models for Efficient Time Series Forecasting

Time series forecasting is an actively researched problem with diverse applications. Recent work has shown that simple linear models can compete with complex deep learning architectures in terms of forecasting accuracy. This has led to the design of several small models, yet the reasons behind their effectiveness remain insufficiently understood. We address this gap through a theoretical framework grounded in reduced-rank regression and kernel analysis. We show both analytically and empirically that the intrinsic complexity of many TSF tasks is lower than commonly assumed and that the performance of linear models is linked to their alignment with low-rank data structures. Building on these insights, we propose a new design for low-rank neural networks that incur lower computational cost than linear models. Specifically, we introduce a simple filter bank architecture that provides a principled way to control model complexity through tunable and interpretable hyperparameters that directly correspond to the rank of the forecasting model. The proposed architecture also serves as a versatile building block for constructing deeper networks. Our evaluation shows that filter bank architectures achieve state-of-the-art results on most long-term TSF benchmarks, with lower computational cost than recently proposed solutions.