Crude oil price forecasting by integrating quantile regression, transformer, and non-dominated sorting dung beetle optimiser

Crude oil prices are influenced by a variety of factors, exhibiting complex volatility and nonlinear characteristics, which pose significant challenges for accurate forecasting. Thus, this study constructs a deterministic and probabilistic forecasting framework for crude oil price using feature screening techniques, Transformer, multi-objective optimisation algorithm, and quantile regression method. Specifically, this study first deeply explores and identifies the key factors affecting crude oil prices from multiple dimensions, such as energy, market, economy and politics, with the help of the least absolute shrinkage and selection operator method. Subsequently, this paper innovatively proposes a quantile Transformer model with its hyperparameters optimised by the non-dominated sorting dung beetle optimiser algorithm, aiming to achieve accurate prediction of crude oil price. Ultimately, by applying kernel density estimation techniques, the approximate distribution of the prediction results is efficiently fitted, thereby deriving the probability density function. The West Texas Intermediate and Brent crude oil price datasets as regarded as two case studies, and the results show that the developed model can significantly outperform the benchmark method in both deterministic and probabilistic forecasting, which not only improves the forecasting accuracy, but also provides valuable insight and guidance in the crude oil market.