# Crude Oil Price Forecasting Model Based on Neural Networks and Error Correction
## 3 Experiments
### Experimental Evaluation of the Proposed Model
#### 3.3.3 Comparison with Diverse Decomposition Methods
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Series**} & \multirow{2}{*}{**Models**} & \multirow{2}{*}{
\begin{tabular}{c} **Decomposition** \\ **Methods** \\ \end{tabular} } & \multirow{2}{*}{**MAE (USD)**} & \multirow{2}{*}{**MAPE (\%)**} & \multirow{2}{*}{**RMSE (USD)**} \\ \hline \multirow{4}{*}{\#1} & Model 4 & - & 0.7119 & 1.1082 & 0.9691 \\  & Model 6 & WPD & 0.2239 & 0.3538 & 0.2671 \\  & Model 7 & VMD & 0.4131 & 0.6228 & 0.5415 \\  & Model 8 & EWT & 0.1728 & 0.2640 & 0.2207 \\ \hline \multirow{4}{*}{\#2} & Model 4 & - & 2.0144 & 4.3907 & 2.6651 \\  & Model 6 & WPD & 0.6911 & 1.5565 & 0.9437 \\  & Model 7 & VMD & 1.1031 & 2.4394 & 1.3172 \\  & Model 8 & EWT & 0.3387 & 0.7625 & 0.4701 \\ \hline \multirow{4}{*}{\#3} & Model 4 & - & 5.2533 & 11.8783 & 6.9218 \\  & Model 6 & WPD & 1.7792 & 4.2214 & 2.4301 \\  & Model 7 & VMD & 3.2493 & 6.6851 & 3.6351 \\ \cline{1-1}  & Model 8 & EWT & 1.6131 & 3.5695 & 1.9352 \\ \hline \hline \end{tabular} Note. Model 4 = SARSA-TCN-GRU-ESN; Model 6 = WPD-SARSA-TCN-GRU-ESN; Model 7 = VMD-SARSA-TCN-GRU-ESN; Model 8 = EWT-SARSA-TCN-GRU-ESN. Series #1, Series #2, and Series #3 refer to three WTI crude oil price datasets with different time spans.  
\end{table} 
Table 7: Evaluation indicators for different decomposition methods across three WTI crude oil price series. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multirow{2}{*}{**Indices**} & \multirow{2}{*}{**Series \#1**} & \multirow{2}{*}{**Series \#2**} & \multirow{2}{*}{**Series \#3**} \\ \hline \multirow{2}{*}{Model 6 vs.} & P\({}_{\text{MAE}}\) (\%) & 68.5490 & 65.6920 & 66.1318 \\  & P\({}_{\text{MAPE}}\) (\%) & 68.0744 & 64.5501 & 64.4612 \\  & P\({}_{\text{RMSE}}\) (\%) & 72.4383 & 64.5904 & 64.8920 \\ \hline \multirow{2}{*}{Model 7 vs.} & P\({}_{\text{MAE}}\) (\%) & 41.9722 & 45.2392 & 38.1474 \\  & P\({}_{\text{MAPE}}\) (\%) & 43.8008 & 44.4417 & 43.7201 \\  & P\({}_{\text{RMSE}}\) (\%) & 44.1234 & 50.5760 & 47.4833 \\ \hline \multirow{2}{*}{Model 8 vs.} & P\({}_{\text{MAE}}\) (\%) & 75.7269 & 83.1861 & 69.2936 \\  & P\({}_{\text{RMSE}}\) (\%) & 76.1776 & 82.6337 & 69.9494 \\ \cline{1-1}  & P\({}_{\text{RMSE}}\) (\%) & 72.2263 & 82.3609 & 72.0420 \\ \hline \hline \end{tabular} Note. Model 4 = SARSA-TCN-GRU-ESN; Model 6 = WPD-SARSA-TCN-GRU-ESN; Model 7 = VMD-SARSA-TCN-GRU-ESN; Model 8 = EWT-SARSA-TCN-GRU-ESN. This table shows the promoting percentages of evaluation indicators for different decomposition methods compared to the SARSA-based ensemble. Series #1, Series #2, and Series #3 refer to three WTI crude oil price datasets with different time spans.  
\end{table} 
Table 8: Promoting percentages for decomposition algorithms. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Series**} & \multirow{2}{*}{
\begin{tabular}{c} **Decomposition** \\ **Methods** \\ \end{tabular} } & \multirow{2}{*}{**MAE (USD)**} & \multirow{2}{*}{**MAPE (\%)**} & \multirow{2}{*}{**RMSE (USD)**} \\ \cline{3-4}  & & WPD & 0.1353 & 0.1619 & 0.1527 \\  & & VMD & 0.3731 & 0.4492 & 0.4913 \\  & & EWT & 0.0975 & 0.1013 & 0.1434 \\ \hline \multirow{4}{*}{\#2} & WPD & 1.1731 & 1.0752 & 1.5963 \\  & VMD & 2.3832 & 1.8923 & 2.4435 \\  & EWT & 0.9816 & 0.4352 & 0.7369 \\ \hline \multirow{4}{*}{\#3} & WPD & 7.1536 & 6.7949 & 6.8753 \\  & VMD & 15.4031 & 16.7098 & 15.2039 \\ \cline{1-1}  & EWT & 5.0524 & 4.1983 & 4.7721 \\ \hline \hline \end{tabular} Note. The table shows MSEI, MSE2, and MSE3, which are the prediction results of each predictor on the decomposed data before using the ensemble model.  
\end{table} 
Table 9: MSE with its components MSE1, MSE2, MSE3. * ECM decomposition can effectively correct prediction residuals. In three different datasets, model 9 reduces the \(P_{MAE}(\%)\), \(P_{MAPE}(\%)\) and \(P_{RMSE}(\%)\) of model 8 by more than 15%. This indicates that the ECM could well excavate the predictable components hidden in the residuals and improve forecasting performance. * Each module of our proposed model can effectively reduce prediction errors.