Building prediction intervals for time series forecasting problems presents a
complex challenge, particularly when relying solely on point predictors, a
common scenario for practitioners in the industry. While research has primarily
focused on achieving increasingly efficient valid intervals, we argue that,
when evaluating a set of intervals, traditional measures alone are
insufficient. There are additional crucial characteristics: the intervals must
vary in length, with this variation directly linked to the difficulty of the
prediction, and the coverage of the interval must remain independent of the
difficulty of the prediction for practical utility. We propose the
Heteroscedastic Quantile Regression (HQR) model and the Width-Adaptive
Conformal Inference (WACI) method, providing theoretical coverage guarantees,
to overcome those issues, respectively. The methodologies are evaluated in the
context of Electricity Price Forecasting and Wind Power Forecasting,
representing complex scenarios in time series forecasting. The results
demonstrate that HQR and WACI not only improve or achieve typical measures of
validity and efficiency but also successfully fulfil the commonly ignored
mentioned characteristics.

通过提出 HQR 模型和 WACI 方法，我们在电力价格预测等复杂时间序列预测场景中评估预测间隔的有效性、效率以及关键特征的满足，克服了仅依靠点预测器构建预测间隔的复杂挑战。