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.

翻译：为时间序列预测问题构建预测区间提出了一个复杂的挑战，尤其是在仅依赖点预测器的情况下——这是业界从业者常见的场景。尽管研究主要集中于实现越来越高效的有效区间，但我们认为，在评估一组区间时，仅靠传统度量标准是不够的。还存在其他关键特性：区间长度必须变化，且这种变化应与预测的难度直接相关；同时，为了实际效用，区间的覆盖度必须独立于预测的难度。我们分别提出了异方差分位数回归模型和宽度自适应共形推断方法，以解决这些问题，并提供了理论上的覆盖度保证。这些方法在代表时间序列预测中复杂场景的电价预测和风电功率预测背景下进行了评估。结果表明，HQR和WACI不仅改进或达到了有效性和效率的典型度量标准，而且成功地满足了通常被忽视的上述特性。