# Conformal prediction for time series

arXiv: https://arxiv.org/abs/2010.09107 · HTML: https://mlsanity.com/paper/2010.09107/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2020.

## Built on by (most cited first, 30 of 53)

- [SAFE: Multitask Failure Detection for Vision-Language-Action Models](https://mlsanity.com/paper/2506.09937/) (2025)
- [Can We Detect Failures Without Failure Data? Uncertainty-Aware Runtime Failure Detection for Imitation Learning Policies](https://mlsanity.com/paper/2503.08558/) (2025)
- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Trustworthy Classification through Rank-Based Conformal Prediction Sets](https://mlsanity.com/paper/2407.04407/) (2024)
- [Out-of-Distribution Generalization in Time Series: A Survey](https://mlsanity.com/paper/2503.13868/) (2025)
- [Kernel-based Optimally Weighted Conformal Time-Series Prediction](https://mlsanity.com/paper/2405.16828/) (2024)
- [Error-quantified Conformal Inference for Time Series](https://mlsanity.com/paper/2502.00818/) (2025)
- [Relational Conformal Prediction for Correlated Time Series](https://mlsanity.com/paper/2502.09443/) (2025)
- [Predictive inference for time series: why is split conformal effective despite temporal dependence?](https://mlsanity.com/paper/2510.02471/) (2025)
- [UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregation](https://mlsanity.com/paper/2306.16549/) (2023)
- [Can Transformers Do Enumerative Geometry?](https://mlsanity.com/paper/2408.14915/) (2024)
- [Distribution-Free Conformal Joint Prediction Regions for Neural Marked Temporal Point Processes](https://mlsanity.com/paper/2401.04612/) (2024)
- [Transformer Conformal Prediction for Time Series](https://mlsanity.com/paper/2406.05332/) (2024)
- [On-line conformalized neural networks ensembles for probabilistic forecasting of day-ahead electricity prices](https://mlsanity.com/paper/2404.02722/) (2024)
- [Flow-based Conformal Prediction for Multi-dimensional Time Series](https://mlsanity.com/paper/2502.05709/) (2025)
- [Non-exchangeable Conformal Prediction with Optimal Transport: Tackling Distribution Shifts with Unlabeled Data](https://mlsanity.com/paper/2507.10425/) (2025)
- [ResCP: Reservoir Conformal Prediction for Time Series Forecasting](https://mlsanity.com/paper/2510.05060/) (2025)
- [Conformal Inference for Time Series over Graphs](https://mlsanity.com/paper/2510.11049/) (2025)
- [Uncertainty quantification in metric spaces](https://mlsanity.com/paper/2405.05110/) (2024)
- [Estimating stationary mass, frequency by frequency](https://mlsanity.com/paper/2503.12808/) (2025)
- [Conformal Predictions for Longitudinal Data](https://mlsanity.com/paper/2310.02863/) (2023)
- [JANET: Joint Adaptive predictioN-region Estimation for Time-series](https://mlsanity.com/paper/2407.06390/) (2024)
- [Topology-Aware Conformal Prediction for Stream Networks](https://mlsanity.com/paper/2503.04981/) (2025)
- [Conformal Prediction with Corrupted Labels: Uncertain Imputation and Robust Re-weighting](https://mlsanity.com/paper/2505.04733/) (2025)
- [On the Performance of LLMs for Real Estate Appraisal](https://mlsanity.com/paper/2506.11812/) (2025)
- [Anytime-Valid Answer Sufficiency Certificates for LLM Generation via Sequential Information Lift](https://mlsanity.com/paper/2510.06478/) (2025)
- [Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces](https://mlsanity.com/paper/2507.15741/) (2025)
- [Enhanced Renewable Energy Forecasting using Context-Aware Conformal Prediction](https://mlsanity.com/paper/2510.15780/) (2025)
- [A general framework for multi-step ahead adaptive conformal heteroscedastic time series forecasting](https://mlsanity.com/paper/2207.14219/) (2022)

## Abstract (arXiv)

We develop a general framework for constructing distribution-free prediction intervals for time series. Theoretically, we establish explicit bounds on conditional and marginal coverage gaps of estimated prediction intervals, which asymptotically converge to zero under additional assumptions. We obtain similar bounds on the size of set differences between oracle and estimated prediction intervals. Methodologically, we introduce a computationally efficient algorithm called textttEnbPI that wraps around ensemble predictors, which is closely related to conformal prediction (CP) but does not require data exchangeability. textttEnbPI avoids data-splitting and is computationally efficient by avoiding retraining and thus scalable to sequentially producing prediction intervals. We perform extensive simulation and real-data analyses to demonstrate its effectiveness compared with existing methods. We also discuss the extension of textttEnbPI on various other applications.