# Crude Oil Price Forecasting Model Based on Neural Networks and Error Correction
## 1 Introduction
The ensemble method blends different base predictors to reduce forecasting errors. One common ensemble approach is the heuristic method [21]. [PERSON] et al. proposed a hybrid model with particle swarm optimization (PSO) [22]. Their experiments on corn and wheat future price series showed better results than other methods. [PERSON] et al. used the sine cosine algorithm-whale optimization algorithm (SCWOA) to optimize the weights of four deep learning methods [23]. Experiments showed that the accuracy of this model was superior to that of all single models. [PERSON] et al. applied gray wolf optimization (GWO) to optimize the weights of base predictors [24]. They found that GWO effectually reduced the prediction errors. These methods underscore the importance of mixing different strategies to improve the crude oil price forecasting performance. In summary, scholars have made many important advances in crude oil price forecasting. Table 1 briefly summarizes the algorithms proposed in these papers, the advantages and disadvantages of the models, and their publication dates. Although lots of effective prediction methods have been proposed in time series prediction, there are still some limitations. There is still some potential to improve the forecasting precision of hybrid models. (1) The heuristic algorithm as a common ensemble learning method has been studied by many scholars, and they have found it difficult to make a breakthrough. Compared with the heuristic algorithm, reinforcement learning (RL) has a strong self-learning ability. Hence, the application of RL in ensemble learning is worth studying. (2) There are still some predictable components in the forecasting residuals of the hybrid model [25]. To further improve the performance of the hybrid model, the residuals can be used to modify prediction results. Therefore, to further improve the accuracy and robustness of crude oil price forecasting, a new prediction method is proposed. This method integrates EWT, three neural networks (TCN, GRU, and ESN), reinforcement learning-based weight optimization, and a final error correction module. The main contributions of this study are as follows. The crude oil price series were adaptively decomposed into multiple subsequences using EWT according to their fluctuation characteristics, reducing nonlinearity and delivering higher predictive accuracy compared with classical decomposition methods. In addition, combining three deep neural networks leveraged their extensive hidden layers to manage non-stationary data and exploit complementary strengths, thereby enhancing both adaptability and generalization in forecasting. The SARSA was employed to optimize the ensemble weights among diverse base predictors. Moreover, a machine learning-based error correction module was applied to address predictable residual components, thereby further improving the accuracy and robustness of crude oil price forecasting. Empirical evaluations on three crude oil price datasets indicate that the model effectively handles nonlinear and volatile market conditions, achieving a mean absolute error (MAE) of USD 0.1239 and a mean absolute percentage error (MAPE) of 0.1914% in the best scenario. Furthermore, additional experiments incorporating abrupt price fluctuations induced by geopolitical events verified the model's adaptability, as it accurately identified mutation points and outperforms advanced benchmarks, reducing the MAE to USD 0.3510 under high volatility. These findings emphasize the potential of this hybrid approach to enhance forecasting accuracy, offering a reliable tool for decision-makers in the energy sector and financial markets. The article is organized as follows. Section 2 elaborates on the structure of our proposed model and the theoretical knowledge involved. Section 3 analyzes the crude oil price data and conducts corresponding comparative experiments. The application analysis of the proposed model is shown in Section 4. The conclusions and future research related to this article are outlined in Section 5.