# Ensemble Conformalized Quantile Regression for Probabilistic Time Series Forecasting

arXiv: https://arxiv.org/abs/2202.08756 · HTML: https://mlsanity.com/paper/2202.08756/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 41 references that are in the map.
- First posted on arXiv 17 Feb 2022.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Learning by Transduction](https://mlsanity.com/paper/1301.7375/) (2013)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [How to Construct Deep Recurrent Neural Networks](https://mlsanity.com/paper/1312.6026/) (2013)
- [Probabilistic Forecasting with Temporal Convolutional Neural Network](https://mlsanity.com/paper/1906.04397/) (2019)
- [Adaptive, Distribution-Free Prediction Intervals for Deep Networks](https://mlsanity.com/paper/1905.10634/) (2019)
- [Predictive Inference Is Free with the Jackknife+-after-Bootstrap](https://mlsanity.com/paper/2002.09025/) (2020)
- [Conformal Prediction Interval Estimations with an Application to Day-Ahead and Intraday Power Markets](https://mlsanity.com/paper/1905.07886/) (2019)

## Built on by (most cited first, 27 of 27)

- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [A Transformer-based Diffusion Probabilistic Model for Heart Rate and Blood Pressure Forecasting in Intensive Care Unit](https://mlsanity.com/paper/2301.06625/) (2023)
- [How Reliable is Your Regression Model's Uncertainty Under Real-World Distribution Shifts?](https://mlsanity.com/paper/2302.03679/) (2023)
- [Relational Conformal Prediction for Correlated Time Series](https://mlsanity.com/paper/2502.09443/) (2025)
- [On-line conformalized neural networks ensembles for probabilistic forecasting of day-ahead electricity prices](https://mlsanity.com/paper/2404.02722/) (2024)
- [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)
- [Deep Generative Spatiotemporal Engression for Probabilistic Forecasting of Epidemics](https://mlsanity.com/paper/2603.07108/) (2026)
- [Conformal Loss-Controlling Prediction](https://mlsanity.com/paper/2301.02424/) (2023)
- [Conformal Predictions for Longitudinal Data](https://mlsanity.com/paper/2310.02863/) (2023)
- [Conformal time series decomposition with component-wise exchangeability](https://mlsanity.com/paper/2406.16766/) (2024)
- [Conformal Prediction for Electricity Price Forecasting in the Day-Ahead and Real-Time Balancing Market](https://mlsanity.com/paper/2502.04935/) (2025)
- [Test-time augmentation improves efficiency in conformal prediction](https://mlsanity.com/paper/2505.22764/) (2025)
- [MetaSTNet: Multimodal Meta-learning for Cellular Traffic Conformal Prediction](https://mlsanity.com/paper/2505.21553/) (2025)
- [A general framework for multi-step ahead adaptive conformal heteroscedastic time series forecasting](https://mlsanity.com/paper/2207.14219/) (2022)
- [Probabilistic load forecasting with Reservoir Computing](https://mlsanity.com/paper/2308.12844/) (2023)
- [Deep sub-ensembles meets quantile regression: uncertainty-aware imputation for time series](https://mlsanity.com/paper/2312.01294/) (2023)
- [Beyond Fixed False Discovery Rates: Post-Hoc Conformal Selection with E-Variables](https://mlsanity.com/paper/2604.11305/) (2026)
- [FEG-Pro: Forecast-Error Growth Profiling for Finite-Horizon Instability Analysis of Nonlinear Time Series](https://mlsanity.com/paper/2605.17282/) (2026)
- [Interval Forecasts for Gas Prices in the Face of Structural Breaks -- Statistical Models vs. Neural Networks](https://mlsanity.com/paper/2407.16723/) (2024)
- [Improving Coverage in Combined Prediction Sets with Weighted p-values](https://mlsanity.com/paper/2505.11785/) (2025)
- [The Evolution of Probabilistic Price Forecasting Techniques: A Review of the Day-Ahead, Intra-Day, and Balancing Markets](https://mlsanity.com/paper/2511.05523/) (2025)
- [Questioning the Coverage-Length Metric in Conformal Prediction: When Shorter Intervals Are Not Better](https://mlsanity.com/paper/2601.21455/) (2026)
- [Conformalized Super Learner](https://mlsanity.com/paper/2604.22391/) (2026)
- [Learning Context-conditioned Gaussian Overbounds for Convolution-Based Uncertainty Propagation](https://mlsanity.com/paper/2605.15789/) (2026)
- [Climate-Invariant Conformal Prediction Intervals for Multi-Horizon Solar and Wind Forecasting](https://mlsanity.com/paper/2607.11470/) (2026)

## Abstract (arXiv)

This paper presents a novel probabilistic forecasting method called ensemble conformalized quantile regression (EnCQR). EnCQR constructs distribution-free and approximately marginally valid prediction intervals (PIs), which are suitable for nonstationary and heteroscedastic time series data. EnCQR can be applied on top of a generic forecasting model, including deep learning architectures. EnCQR exploits a bootstrap ensemble estimator, which enables the use of conformal predictors for time series by removing the requirement of data exchangeability. The ensemble learners are implemented as generic machine learning algorithms performing quantile regression, which allow the length of the PIs to adapt to local variability in the data. In the experiments, we predict time series characterized by a different amount of heteroscedasticity. The results demonstrate that EnCQR outperforms models based only on quantile regression or conformal prediction, and it provides sharper, more informative, and valid PIs.