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

TL;DR

This paper introduces a novel method combining Heteroscedastic Quantile Regression with Width-Adaptive Conformal Inference to produce reliable, adaptive prediction intervals for time series forecasting, ensuring coverage and efficiency.

Contribution

It presents an integrated approach that guarantees coverage and adapts interval widths based on predictive uncertainty, addressing limitations of existing methods.

Findings

Method guarantees theoretical coverage.

Achieves superior efficiency compared to benchmarks.

Effective in synthetic and real-world electricity forecasting.

Abstract

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.