Probabilistic oil price forecasting with a variational mode decomposition-gated recurrent unit model incorporating pinball loss

Prediction methods have garnered significant attention in intelligent decision-making. Most existing approaches to predicting crude oil prices prioritize accuracy and stability while providing precise prediction intervals that can offer valuable insights. Thus far, we introduced a novel hybrid model to forecast future crude oil prices. Our approach leverages the variational mode decomposition (VMD) to simplify the complexity of the original time series, yielding a set of subseries. These subseries are then modeled using a deep neural network architecture called a gated recurrent unit (GRU). To address the prediction uncertainty, we employed the pinball loss function rather than the mean square error to guide the proposed VMD-GRU. This adaptation extends the traditional GRU-based point forecasting to probabilistic forecasting by estimating quantiles. We evaluated our proposed model on a well-established crude oil price series by conducting both single- and multi-step-ahead forecasting analyses. Our findings underscore the efficacy of the combined model, demonstrating its superior predictive performance compared to benchmark models.