We propose a simple and efficient approach to generate a prediction intervals (PI) for approximated and forecasted trends. Our method leverages a weighted asymmetric loss function to estimate the lower and upper bounds of the PI, with the weights determined by its coverage probability. 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且高效的方法，用于生成近似和预测趋势的预测区间（PI）。该方法利用加权非对称损失函数来估计预测区间上下界，其中权重由预测区间的覆盖概率决定。我们给出了该方法的简洁数学证明，展示了如何将其扩展以推导参数化函数的预测区间，并论证了该方法为何适用于预测因变量的预测区间。基于神经网络模型的实际预测任务测试结果表明，该方法能够在复杂的机器学习场景下生成可靠的预测区间。