Prediction intervals for neural network models using weighted asymmetric loss functions

We develop a novel and simple method to produce prediction intervals (PIs) for fitting and forecasting exercises. It finds the lower and upper bound of the intervals by minimising a weighted asymmetric loss function, where the weight depends on the width of the interval. We give a short mathematical proof. As a corollary of our proof, we find PIs for values restricted to a parameterised function and argue why the method works for predicting PIs of dependent variables. The results of applying the method on a neural network deployed in a real-world forecasting task prove the validity of its practical implementation in complex machine learning setups.