Position: Why a Dynamical Systems Perspective is Needed to Advance Time Series Modeling
arXiv:2602.16864v1 Announce Type: new Abstract: Time series (TS) modeling has come a long way from early statistical, mainly linear, approaches to the current trend in TS foundation models. With a lot of hype and industrial demand in this field, it is not always clear how much progress there really is. To advance TS forecasting and analysis to the next level, here we argue that the field needs a dynamical systems (DS) perspective. TS of observations from natural or engineered systems almost always originate from some underlying DS, and arguably access to its governing equations would yield theoretically optimal forecasts. This is the promise of DS reconstruction (DSR), a class of ML/AI approaches that aim to infer surrogate models of the underlying DS from data. But models based on DS principles offer other profound advantages: Beyond short-term forecasts, they enable to predict the long-term statistics of an observed system, which in many practical scenarios may be the more relevant
arXiv:2602.16864v1 Announce Type: new Abstract: Time series (TS) modeling has come a long way from early statistical, mainly linear, approaches to the current trend in TS foundation models. With a lot of hype and industrial demand in this field, it is not always clear how much progress there really is. To advance TS forecasting and analysis to the next level, here we argue that the field needs a dynamical systems (DS) perspective. TS of observations from natural or engineered systems almost always originate from some underlying DS, and arguably access to its governing equations would yield theoretically optimal forecasts. This is the promise of DS reconstruction (DSR), a class of ML/AI approaches that aim to infer surrogate models of the underlying DS from data. But models based on DS principles offer other profound advantages: Beyond short-term forecasts, they enable to predict the long-term statistics of an observed system, which in many practical scenarios may be the more relevant quantities. DS theory furthermore provides domain-independent theoretical insight into mechanisms underlying TS generation, and thereby will inform us, e.g., about upper bounds on performance of any TS model, generalization into unseen regimes as in tipping points, or potential control strategies. After reviewing some of the central concepts, methods, measures, and models in DS theory and DSR, we will discuss how insights from this field can advance TS modeling in crucial ways, enabling better forecasting with much lower computational and memory footprints. We conclude with a number of specific suggestions for translating insights from DSR into TS modeling.
Executive Summary
This article argues that incorporating a dynamical systems (DS) perspective is essential for advancing time series (TS) modeling. By leveraging DS theory, TS forecasting and analysis can be elevated to the next level. The authors contend that accessing the governing equations of the underlying DS would yield theoretically optimal forecasts, and that DS models offer advantages such as predicting long-term statistics and providing domain-independent theoretical insights. The article reviews central concepts, methods, measures, and models in DS theory and DS reconstruction (DSR), and discusses how DS insights can improve TS modeling with reduced computational and memory footprints.
Key Points
- ▸ Time series modeling has made significant progress but needs a dynamical systems perspective to advance forecasting and analysis.
- ▸ Dynamical systems theory offers theoretically optimal forecasts and predicts long-term statistics.
- ▸ Dynamical systems models provide domain-independent theoretical insights into mechanisms underlying time series generation.
Merits
Strength in Predictive Power
Dynamical systems models offer potentially more accurate forecasts by leveraging the governing equations of the underlying system.
Reduced Computational Footprint
Dynamical systems models can reduce computational and memory requirements for time series forecasting and analysis.
Domain-Independent Insights
Dynamical systems theory provides domain-independent insights into mechanisms underlying time series generation, offering a unified understanding of complex systems.
Demerits
Complexity of Dynamical Systems
Dynamical systems models can be mathematically complex and challenging to interpret, requiring advanced expertise in mathematical and computational methods.
Data Requirements
Dynamical systems reconstruction (DSR) requires large amounts of data to accurately infer the governing equations of the underlying system.
Interpretability Challenges
Dynamical systems models can be difficult to interpret, making it challenging to understand the underlying mechanisms driving time series behavior.
Expert Commentary
This article offers a compelling case for incorporating a dynamical systems perspective into time series modeling. By leveraging DS theory, researchers and practitioners can gain a deeper understanding of complex systems and develop more accurate and efficient forecasting models. However, the complexity of dynamical systems models and the challenges of data requirements and interpretability must be carefully considered. The article's suggestions for translating insights from DSR into TS modeling offer a valuable roadmap for future research and development.
Recommendations
- ✓ Recommendation 1: Develop and apply advanced mathematical and computational methods to simplify the interpretation and application of dynamical systems models.
- ✓ Recommendation 2: Investigate the use of domain adaptation and transfer learning techniques to enable the application of DS models in diverse domains and scenarios.
