Probabilistic interval prediction method based on shape‐adaptive quantile regression

Abstract This article introduces customized screening ensemble with shape‐adaptive quantile regression (CseAQR), a novel probabilistic interval forecasting method built upon the quantile regression model. CseAQR utilizes ensemble learning to perform adaptive quantile regression prediction, which can handle the heteroscedasticity feature in time series data by using a weighted adaptive allocation loss function to enhance the adaptability of the basic quantile regression model on the dataset. The model performance predictor is used to select the optimal ensemble learner combination, assign reasonable adaptive weights to it, and obtain a preliminary prediction interval through weighted aggregation. Combining ensemble learners not only improves the accuracy and robustness of prediction intervals but also ensures the commutativity required for conformal prediction. Finally, the conformal prediction method is applied to locally adjust the prediction interval, constructing a more consistently aligned prediction interval with the actual data on a narrower basis.