We propose a simple and efficient approach to generate prediction intervals (PIs) for approximated and forecasted trends. Our method leverages a weighted asymmetric loss function to estimate the lower and upper bounds of the PIs, with the weights determined by the interval width. We provide a concise mathematical proof of the method, show how it can be extended to derive PIs for parametrised functions and argue why the method works for predicting PIs of dependent variables. The presented tests of the method on a real-world forecasting task using a neural network-based model show that it can produce reliable PIs in complex machine learning scenarios.

翻译：我们提出了一种简单高效的生成预测区间（PIs）的方法，用于近似和预测趋势。该方法利用加权非对称损失函数来估计预测区间的上下界，其中权重由区间宽度决定。我们提供了该方法的简洁数学证明，展示了如何将其扩展为参数化函数推导预测区间，并论证了该方法为何适用于预测因变量的预测区间。在基于神经网络模型的真实预测任务中对方法进行的测试表明，它能够在复杂的机器学习场景中生成可靠的预测区间。