## 3 Experimental Analysis
### Proposed Model Results
#### 3.4.2 Model Rationalization Experiment in Our Method  
In order to rationalize the contribution of each module within our proposed method to the overall performance, this study conducted a Model Rationalization Experiment considering the use of VMD, the presence or exclusive use of the SARIMA module, and the use of the TimesNet model. The results are shown in Table 4.  
From the data in the above table, we obtained the following three points:  
(1) The proposed model significantly outperforms the SARIMA-only model, achieving a 49.61% improvement in the MAE and a 52.34% improvement in the RMSE. This indicates that the integration of additional components beyond SARIMA provides a substantial enhancement in prediction accuracy.  
(2) When comparing the proposed model to the I-TimesNet model without the SARIMA module, we observe a 49.64% improvement in the MAE and a 52.37% improvement in the RMSE. This suggests that the SARIMA module plays a key role in enhancing the time series modeling capabilities of the I-TimesNet architecture.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Part** & **MAE** & **RMSE** \\ \hline Proposed & 0.2253 & 0.3178 \\ SARIMA & 0.4479 & 0.6667 \\ I\_TimesNet & 0.2803 & 0.4181 \\ VMD-I\_TimesNet & 0.3106 & 0.4320 \\ VMD-SARIMA & 0.2806 & 0.3822 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Model Rationalization Experiment result.  
Figure 10: January 25 th forecasting performance fit graph.  
(3) Without VMD, the proposed method's performance drops by 19.63% in the MAE and 24.15% in the RMSE, indicating that VMD is crucial for effectively handling the different frequency components in the data. In order to further investigate the impact of each module on different time periods, we refined the time nodes and categorized the multiple time periods of the day into morning peak hours, evening peak hours, and normal hours. Specifically, the morning peak hour was defined as 7 a.m.-9 a.m., the evening peak hour was defined as 5 p.m.-7 p.m., and the rest of the day was considered as the regular hours. The results of the ablation experiments can be further obtained from the detailed ablation experiment table, as shown in Table 5 (best performance is marked in red, and second-best performance is underlined).  
As shown in Table 5, the SARIMA model performs relatively poorly for the morning and evening peak hours, with MAE values of 1.4445 and 1.1110, respectively, which may be attributed to the model's limited ability to capture sudden changes in passenger flow, which are common during peak hours. In contrast, the SARIMA model performs better during normal hours with a lower MAE value of 0.3353, but its linear nature may not be able to account for the nonlinear and sudden fluctuations that are typical of peak hours.  
When using the I-TimesNet model alone, it has limited predictive power during the peak hours, with MAE values of 0.5666 and 0.8192 for the morning and evening peaks, respectively; however, when combined with the VMD (VMD-I_TimesNet), its performance improves dramatically, with the MAE values dropping to 0.6389 and 0.4078, respectively, which suggests that the VMD module helps the I-TimesNet model to better capture sudden changes in passenger flow.  
Similarly, after adding the VMD module to the SARIMA model (VMD-SARIMA), the prediction accuracies of all time periods are significantly improved. During the morning and evening peaks, the MAE values drop to 0.4207 and 0.4303, respectively, which indicates that the VMD effectively improves the model performance by extracting the relevant sequence information.  
Overall, the combination of the SARIMA model, I-TimesNet model, and VMD consistently outperforms the other models in almost all time periods except for the evening peak, with the lowest MAE value of 0.3626 in the morning peak, which suggests that the integration of these components can effectively capture the complex patterns of the metro passenger flow in the peak hours.