# Crude Oil Price Forecasting Model Based on Neural Networks and Error Correction
## 1 Introduction  
Crude oil is a key strategic resource for social and economic development. It remains important in global industrial production, even though alternative energy sources exist [1]. In addition, crude oil price volatility has an important impact on economic growth, securities markets, and national security. Efficient and accurate crude oil price forecasting contributes to global economic development. However, the price is affected by lots of factors, including geopolitical conflicts, oil production, and the pace of economic development [2]. Hence, crude oil price data are highly nonlinear, non-stationary, and stochastic. To precisely forecast the crude oil price, researchers have made lots of contributions [3]. Common crude oil price forecasting models include causal relationship forecasting models, statistical models, machine learning models, and hybrid forecasting models [4]. The causal relationships model selects several independent variables to predict future values, but it needs many data sources, and complicated factors, high research costs, and interactions between independent variables limit its use [5]. The current international situation changes quickly, and slow updates make the causal relationships model less suited to short-term forecasting. Statistical models, in contrast, have simpler structures and meet short-term speed needs. Typical statistical methods include the autoregressive integrated moving average (ARIMA) [6], and gray models (GM) [7]. Yet crude oil prices often show strong nonlinearity. Hence, such statistical models may fail to capture sudden or large price swings. This problem makes accurate prediction difficult. As global markets grow more volatile, better approaches are needed to handle complex data patterns. Many scholars use deep learning models to predict time series [8; 9; 10; 11]. [PERSON] et al. employed a deep neural network (DNN) model to forecast equity premiums [8]. Theycompared the DNN model with ordinary least squares (OLS) and historical average (HA) models. Experimental findings indicated that the DNN model demonstrated superior predictive performance. [PERSON] et al. performed short-term forecasts of WTI and Brent crude oil prices using long short-term memory (LSTM) networks by reducing the influence of historical data while increasing that of current data. Their results showed that this approach produced lower prediction errors [12]. [PERSON] et al. compared the predictive performance of a gated recurrent unit (GRU) model with that of a single LSTM network, revealing that GRU effectively reduced prediction errors in crude oil price models [13]. Additionally, several studies employed group method of data handling (GMDH) networks for time series forecasting and reported favorable results on respective datasets [14; 15]. [PERSON] et al. implemented 16 deep learning architectures to predict daily oil prices for WTI and Brent. Their findings indicated that the temporal convolutional network (TCN) surpassed the other models [16]. However, a single machine learning model may not adapt well to all time series conditions. Therefore, more researchers turn to hybrid forecasting models. Two common approaches in crude oil price forecasting are the decomposition algorithm and the ensemble algorithm [17]. The decomposition method handles raw crude oil price data, which are nonlinear and random. [PERSON] et al. used integrated empirical mode decomposition (EEMD) to preprocess crude oil prices [18]. Experimental results showed that this decomposition method could effectively improve the accuracy of convolutional neural networks (CNNs) and LSTM networks. [PERSON] et al. adopted variational modal decomposition (VMD) to process original data, then used an artificial neural network for each sub-series [19]. Their results showed reduced prediction errors. [PERSON] et al. applied complementary EEMD (CEEMD) to split crude oil data into multiple subsequences [20]. It could be seen that the method improved the recognition ability for nonlinear data of the GRU.