Position: Why a Dynamical Systems Perspective is Needed to Advance Time Series Modeling
This work addresses a fundamental limitation in current time series modeling approaches: their general lack of grounding in the underlying dynamical systems, which impedes long-term statistical forecasting, generalization to unseen regimes (e.g., critical transitions), and sample-efficient learning. The paper presents the first systematic argument for the foundational value of a dynamical systems perspective in time series modeling and introduces a novel paradigm—Dynamical System Reconstruction (DSR)—that infers latent dynamical mechanisms directly from observational data. This approach substantially enhances model interpretability, generalization capability, and computational efficiency, enabling reliable long-horizon prediction, theoretical performance bound analysis, and effective modeling under low-data regimes. The framework provides both theoretical foundations and practical pathways toward next-generation foundation models for time series.