# Enhancing reliability in prediction intervals using point forecasters: Heteroscedastic Quantile Regression and Width-Adaptive Conformal Inference

arXiv: https://arxiv.org/abs/2406.14904 · HTML: https://mlsanity.com/paper/2406.14904/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 21 Jun 2024.

## Builds on (most cited first, 20 of 20)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark](https://mlsanity.com/paper/2008.08004/) (2020)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [A Second-order Bound with Excess Losses](https://mlsanity.com/paper/1402.2044/) (2014)
- [NGBoost: Natural Gradient Boosting for Probabilistic Prediction](https://mlsanity.com/paper/1910.03225/) (2019)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Improving Conditional Coverage via Orthogonal Quantile Regression](https://mlsanity.com/paper/2106.00394/) (2021)
- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [Optimal learning with Bernstein Online Aggregation](https://mlsanity.com/paper/1404.1356/) (2014)
- [Forecast combinations: an over 50-year review](https://mlsanity.com/paper/2205.04216/) (2022)
- [Split Localized Conformal Prediction](https://mlsanity.com/paper/2206.13092/) (2022)
- [Day-ahead electricity price forecasting with high-dimensional structures: Univariate vs. multivariate modeling frameworks](https://mlsanity.com/paper/1805.06649/) (2018)
- [Conformal Prediction Interval Estimations with an Application to Day-Ahead and Intraday Power Markets](https://mlsanity.com/paper/1905.07886/) (2019)

## Abstract (arXiv)

Constructing prediction intervals for time series forecasting is challenging, particularly when practitioners rely solely on point forecasts. While previous research has focused on creating increasingly efficient intervals, we argue that standard measures alone are inadequate. Beyond efficiency, prediction intervals must adapt their width based on the difficulty of the prediction while preserving coverage regardless of complexity. To address these issues, we propose combining Heteroscedastic Quantile Regression (HQR) with Width-Adaptive Conformal Inference (WACI). This integrated procedure guarantees theoretical coverage and enables interval widths to vary with predictive uncertainty. We assess its performance using both a synthetic example and a real world Electricity Price Forecasting scenario. Our results show that this combined approach meets or surpasses typical benchmarks for validity and efficiency, while also fulfilling important yet often overlooked practical requirements.