## 4 Experimental Results
### Experimental Results Analysis
#### 4.2.4 Stacking Experimental Results  
The stacking ensemble model was constructed by integrating the results of four experiments, each under different feature combinations for the three backbone models (Informer, MLR, SVR), resulting in a total of 12 base models. Stacking effectively captures feature relationships and patterns in the data by using the prediction results of the base models (i.e., the outputs of the first layer) as new input features for the second layer meta-learner. This approach enables the effective combination of the strengths of multiple models, thereby enhancing the overall prediction accuracy. The performance evaluation and prediction results of the stacking ensemble model are shown in Table 9 and Figure 8.  
In Table 9, the performance evaluation results of the stacking ensemble model are compared with the optimal feature combinations (\(R^{2}\)) of the INF, MLR, and SVR. The stacking ensemble model outperforms the base models across all metrics.  
The stacking ensemble model exhibits lower mean relative error (MRE), mean absolute error (MAE), symmetric mean absolute percentage error (SMAPE), and mean absolute percentage error (MAPE). This indicates that the stacking ensemble model has higher accuracy and stability in predicting natural gas purchase volumes, particularly in managing relative errors. Furthermore, the stacking model achieved an \(R^{2}\) of 92.57%, which is about 4-15 percentage points higher than the \(R^{2}\) values of the base models, demonstrating its superior ability to explain the variability in the data. Additionally, the root mean square  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Approach** & **MRE** & **MAE** & **SMAPE** & **\(\mathbf{R^{2}}\) (\%)** & **RMSE** & **MAPE (\%)** \\ \hline INF-RB & 0.0957 & 1,117,435 & 0.1013 & 77.19 & 1,400,524 & 9.75 \\ MLR-RB-UB & 0.0823 & 943,053 & 0.0835 & 82.76 & 1,217,738 & 8.23 \\ SVR-RB & 0.0702 & 817,575 & 0.0718 & 88.60 & 990,176 & 7.02 \\
**Stacking** & 0.0614 & 648,303 & 0.0601 & 92.57 & 799,635 & 6.14 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Performance comparison of optimal feature combinations in base methods and the stacking model.  
Figure 7: Comparison of actual and predicted gas purchase volumes using the SVR model with different feature combinations. (**a**) SVR; (**b**) SVR-RB; (**c**) SVR-UB; and (**d**) SVR-RB-UB.  
error (RMSE) of the stacking model is 799,635, the lowest among all models, indicating the best performance in terms of the square root of the prediction errors and providing the most stable and accurate results.  
Figure 8 illustrates the comparison between the predicted values and the actual values using the stacking ensemble model. As seen in the figure, the prediction results of the stacking ensemble model are very close to the actual values, especially in terms of trend changes and fluctuations.  
These results validate the superiority of the stacking model in the task of predicting natural gas purchase volumes. Compared to individual base models, the stacking model demonstrates higher accuracy across all evaluation metrics, particularly in key indicators such as \(R^{2}\), MRE, MAE, RMSE, and MAPE.