# Sequential Predictive Conformal Inference for Time Series

arXiv: https://arxiv.org/abs/2212.03463 · HTML: https://mlsanity.com/paper/2212.03463/

## Key facts

- Cited by 75 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 38 references that are in the map.
- First posted on arXiv 7 Dec 2022.

## Builds on (most cited first, 15 of 15)

- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [A Comprehensive Analysis of Deep Regression](https://mlsanity.com/paper/1803.08450/) (2018)
- [Conformal Prediction with Temporal Quantile Adjustments](https://mlsanity.com/paper/2205.09940/) (2022)
- [Conformal Anomaly Detection on Spatio-Temporal Observations with Missing Data](https://mlsanity.com/paper/2105.11886/) (2021)

## Built on by (most cited first, 30 of 75)

- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [SAFE: Multitask Failure Detection for Vision-Language-Action Models](https://mlsanity.com/paper/2506.09937/) (2025)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [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)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Kernel-based Optimally Weighted Conformal Time-Series Prediction](https://mlsanity.com/paper/2405.16828/) (2024)
- [Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series](https://mlsanity.com/paper/2402.05203/) (2024)
- [Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations](https://mlsanity.com/paper/2502.14105/) (2025)
- [Normalizing Flows for Conformal Regression](https://mlsanity.com/paper/2406.03346/) (2024)
- [Relational Conformal Prediction for Correlated Time Series](https://mlsanity.com/paper/2502.09443/) (2025)
- [Towards Modeling Uncertainties of Self-explaining Neural Networks via Conformal Prediction](https://mlsanity.com/paper/2401.01549/) (2024)
- [Predictive inference for time series: why is split conformal effective despite temporal dependence?](https://mlsanity.com/paper/2510.02471/) (2025)
- [The Forecast After the Forecast: A Post-Processing Shift in Time Series](https://mlsanity.com/paper/2601.20280/) (2026)
- [Transformer Conformal Prediction for Time Series](https://mlsanity.com/paper/2406.05332/) (2024)
- [CORA: Conformal Risk-Controlled Agents for Safeguarded Mobile GUI Automation](https://mlsanity.com/paper/2604.09155/) (2026)
- [AI4OPT: AI Institute for Advances in Optimization](https://mlsanity.com/paper/2307.02671/) (2023)
- [Spatial Conformal Inference through Localized Quantile Regression](https://mlsanity.com/paper/2412.01098/) (2024)
- [CUQDS: Conformal Uncertainty Quantification under Distribution Shift for Trajectory Prediction](https://mlsanity.com/paper/2406.12100/) (2024)
- [Flow-based Conformal Prediction for Multi-dimensional Time Series](https://mlsanity.com/paper/2502.05709/) (2025)
- [Conformal Prediction for Time-series Forecasting with Change Points](https://mlsanity.com/paper/2509.02844/) (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)
- [Leave a Window Out: Modifying the Jackknife for Predictive Inference in Time Series](https://mlsanity.com/paper/2605.30292/) (2026)
- [Conformal Predictions for Longitudinal Data](https://mlsanity.com/paper/2310.02863/) (2023)
- [DistPred: A Distribution-Free Probabilistic Inference Method for Regression and Forecasting](https://mlsanity.com/paper/2406.11397/) (2024)
- [Conformal time series decomposition with component-wise exchangeability](https://mlsanity.com/paper/2406.16766/) (2024)
- [Uncertainty-Aware Decarbonization for Datacenters](https://mlsanity.com/paper/2407.02390/) (2024)
- [Conformal Prediction for Electricity Price Forecasting in the Day-Ahead and Real-Time Balancing Market](https://mlsanity.com/paper/2502.04935/) (2025)

## Abstract (arXiv)

We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the textitsequential predictive conformal inference (textttSPCI). We specifically account for the nature that time series data are non-exchangeable, and thus many existing conformal prediction algorithms are not applicable. The main idea is to adaptively re-estimate the conditional quantile of non-conformity scores (e.g., prediction residuals), upon exploiting the temporal dependence among them. More precisely, we cast the problem of conformal prediction interval as predicting the quantile of a future residual, given a user-specified point prediction algorithm. Theoretically, we establish asymptotic valid conditional coverage upon extending consistency analyses in quantile regression. Using simulation and real-data experiments, we demonstrate a significant reduction in interval width of textttSPCI compared to other existing methods under the desired empirical coverage.