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

This repository contains the empirical benchmarks, codes, and figures for the paper "Beyond Point Forecasts: A Survey on Probabilistic Forecasting for Time Series and Spatiotemporal Data" by Donia Besher, Rajdeep Pathak, Madhurima Panja, and Tanujit Chakraborty.

📖 Overview

Probabilistic forecasting quantifies predictive uncertainty, which is essential for high-stakes decision-making in domains such as epidemiology, energy, transportation, and environmental science. While current literature typically isolates temporal and spatiotemporal domains, this survey bridges the gap by establishing a cohesive taxonomy that systematically organizes the entire spectrum of existing methodologies.

This repository supports the survey by providing unified empirical evaluations of representative methods, analyzing key trade-offs across predictive accuracy and computational efficiency.

Taxonomy Highlights

• Model-Agnostic Methods: Pre-control limits, Ensemble-based methods, and Distribution-free calibration (Conformal Prediction, Conformalized Quantile Regression).
• Model-Intrinsic Methods: Bayesian Modeling (Hierarchical, State Space, Nonparametric, BNNs), Parametric Predictive Distributions, Distributional Regression (Quantile Regression, Engression, Loss-Driven), and Generative Models (Copulas, HMMs, VAEs, GANs, Normalizing Flows, Diffusion Models).
• Foundation Models: Exploration of zero-shot uncertainty quantification in modern temporal foundation models.

🗂️ Repository Structure

The repository is organized to separate the benchmark codebase from the visualization and forecast data:

├── Experiments/
│   └── Benchmark_Experiments.ipynb  # Contains the code for the empirical benchmark evaluations
├── Figures/
│   ├── Figure_Generators.ipynb      # Notebook for generating the figures used in the survey
│   ├── Forecasts/                   # Benchmark forecast files saved as .npz arrays
│   └── [Figure Image Files]         # Exported figures supporting the paper
├── LICENSE                          # MIT License
└── README.md                        # This file

Experiments

• Experiments/Benchmark_Experiments.ipynb: This core notebook executes the empirical benchmark of representative probabilistic forecasting methods under a unified protocol. It contains the data loading, model initialization, training loops, and evaluation metrics computation.

Figures & Visualizations

• Figures/Figure_Generators.ipynb: Generates the visualizations and comparative plots featured in the survey based on the benchmark results.
• Figures/Forecasts/: Contains the raw output forecasts from the benchmarked models. These are serialized as .npz (NumPy zipped arrays) to ensure efficient storage and easy loading for post-processing and figure generation.

📊 Evaluation Metrics

The benchmark evaluates both point and probabilistic metrics, emphasizing calibration and sharpness, including:

• Continuous Ranked Probability Score (CRPS)
• Winkler Score
• Prediction Interval Coverage Probability (PICP)
• Pinball Loss

📝 Citation

If you find this survey, code, or benchmark useful in your research, please consider citing our paper:

@article{besher2026probabilistic,
  title={Beyond Point Forecasts: A Survey on Probabilistic Forecasting for Time Series and Spatiotemporal Data},
  author={Besher, Donia and Pathak, Rajdeep and Panja, Madhurima and Chakraborty, Tanujit},
  journal={arXiv preprint arXiv:2609.13345},
  year={2026}
}