Beyond Point Forecasts: A Survey on Probabilistic Forecasting for Time Series and Spatiotemporal Data

Abstract:Probabilistic forecasting is central to decision-making under uncertainty, yet its methodological landscape has become increasingly fragmented across temporal and spatiotemporal forecasting, statistical modeling, machine learning, and deep generative modeling. This survey develops a unified perspective by organizing probabilistic forecasting methods according to where and how uncertainty is introduced into the forecasting pipeline. Our taxonomy connects model-agnostic approaches including ensembles and distribution-free calibration, with model-intrinsic approaches spanning Bayesian modeling, parametric predictive distributions, distributional regression, and modern generative models, and further examines the emerging role of time series foundation models. Beyond methodological synthesis, we identify the assumptions, computational demands, and forms of uncertainty represented by different paradigms, and translate these distinctions into data-driven and domain-specific guidance for method selection. We complement the survey with a cross-paradigm empirical study on univariate, multivariate, and spatiotemporal forecasting tasks. The results reveal that no single uncertainty-quantification paradigm dominates across settings. Calibration, sharpness, predictive accuracy, and computational efficiency can lead to substantially different model preferences, while expressive generative models and zero-shot foundation models exhibit markedly different accuracy-efficiency trade-offs. Lastly, we identify unresolved challenges surrounding uncertainty in evolving dependency structures, physics-informed predictive distributions, forecasting extreme events, handling count-valued, directional, and continuous-time series, and the development of unified software resources. Our survey provides both a conceptual framework and a practical roadmap for probabilistic forecasting research.

Machine Learning (stat.ML); Machine Learning (cs.LG); Econometrics (econ.EM); Applications (stat.AP)

arXiv:2609.13345 [stat.ML]

(or arXiv:2609.13345v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.13345 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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