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

Donia Besher, Rajdeep Pathak, Madhurima Panja, Tanujit Chakraborty

arXiv 11 Sep 2026 · Statistics — Machine Learning

arXiv:2609.13345 · PDF · Extracted main text

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.

Citation extraction

392
references
805
in-text mentions
392
distinct cited
14
self-citations
32,958
main-text words

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Rajdeep Pathak and Tanujit Chakraborty (2026) Deep Generative Spatiotemporal Engression for Probabilistic Forecasting of Epidemics self1.000145100%
2Pathak, Rajdeep and Goswami, Rahul and Panja, Madhurima and Ghosh, P… (2026) Deep Generative Transformers for Probabilistic Time Series and Spatiotemporal Forecasting self1.000113100%
3Panja, Madhurima and Chakraborty, Tanujit and Biswas, Anubhab and De… (2026) E-STGCN: extreme spatio-temporal graph convolutional networks for air quality forecasting self1.00096100%
4Xinyao Fan and Yueying Wu and Chang Xu and Yuhao Huang and Weiqing L… (2024) MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Process1.00093100%
5Salinas, David and Bohlke-Schneider, Michael and Callot, Laurent and… (2019) High-dimensional multivariate forecasting with low-rank Gaussian copula processes1.00093100%
6Gneiting, Tilmann and Katzfuss, Matthias (2014) Probabilistic Forecasting1.00083100%
7Panja, Madhurima and D'Agostino, Danny and Li, Huitao and Chakrabort… (2026) EpiCastBench: Datasets and Benchmarks for Multivariate Epidemic Forecasting self1.00073100%
8Jinwen Qiu and S. Rao Jammalamadaka and Ning Ning (2018) Multivariate Bayesian Structural Time Series Model1.00073100%
9Bergsma, Shane and Zeyl, Tim and Rahimipour Anaraki, Javad and Guo,… (2022) C2FAR: Coarse-to-Fine Autoregressive Networks for Precise Probabilistic Forecasting1.00063100%
10Rasul, Kashif and Seward, Calvin and Schuster, Ingmar and Vollgraf,… (2021) Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting1.00063100%

Showing the top 10 of 392 scored citations.