Enhancing reliability in prediction intervals using point forecasters: Heteroscedastic Quantile Regression and Width-Adaptive Conformal Inference
This work addresses the problem of ensuring adaptive and reliable prediction intervals for practitioners in time series forecasting, representing an incremental improvement by integrating existing methods to meet practical requirements.
The paper tackled the challenge of constructing reliable prediction intervals for time series forecasting when only point forecasts are available, by proposing a combination of Heteroscedastic Quantile Regression and Width-Adaptive Conformal Inference, which achieved validity and efficiency meeting or surpassing benchmarks in synthetic and real-world electricity price scenarios.
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.