## 4 Results and Discussion
### Comparison of the Results of Different Prediction Models  
To evaluate the performance of the models, a comparison of the predictive capabilities of the SVR, GRNN, ELM, PSO-SVR, PSO-GRNN, PSO-ELM, SSA-SVR, SSA-GRNN, and SSA-ELM models was made using monthly pork price data from Beijing. The accuracy of the predictions of these ten models was ascertained in accordance with Equations (12)-(16). The fitting effects of the models are presented in Figures 6 and 7, while Table 3 shows the performance of the models based on evaluation metrics such as MAE, MAPE, MSE, RMSE, and TIC. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Prediction Model** & **MAE** & **MAPE** & **MSE** & **RMSE** & **TIC** \\ \hline SVR & 2.82 & 1.38 & 15.16 & 3.89 & 0.66 \\ ELM & 1.42 & 2.31 & 3.10 & 1.76 & 0.21 \\ SSA-SVR & 1.88 & 1.53 & 9.87 & 3.14 & 0.51 \\ SSA-ELM & 0.63 & 1.93 & 0.60 & 0.77 & 0.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The evaluation metrics of four methods regarding the residual prediction. (1) Analysis of the results of single prediction models  
There were different degrees of fluctuations in the prediction results of the SVR, GRNN, and ELM models. The GRNN model achieved the best prediction results, followed by the ELM and SVR models, respectively. The MAE, MAPE, MSE, RMSE, and TIC values of the GRNN model were 3.17, 0.14, 18.45, 4.30, and 0.10, respectively. Relative to the SVR model, the GRNN model exhibited decreases of 75.54% and 50.54% in the MSE and RMSE metrics, respectively. Relative to the ELM model, the GRNN model exhibited decreases of 53.66% \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Prediction Model** & **MAE** & **MAPE** & **MSE** & **RMSE** & **TIC** \\ \hline SVR & 8.04 & 0.43 & 75.43 & 8.69 & 0.17 \\ GRNN & 3.17 & 0.14 & 18.45 & 4.30 & 0.10 \\ ELM & 4.09 & 0.21 & 39.82 & 6.31 & 0.14 \\ PSO-SVR & 6.85 & 0.36 & 54.76 & 7.40 & 0.15 \\ PSO-GRNN & 2.93 & 0.13 & 16.47 & 4.06 & 0.10 \\ PSO-ELM & 2.60 & 0.13 & 10.82 & 3.29 & 0.08 \\ SSA-SVR & 2.64 & 0.12 & 13.42 & 3.66 & 0.09 \\ SSA-GRNN & 2.88 & 0.13 & 15.82 & 3.98 & 0.10 \\ SSA-ELM & 2.18 & 0.10 & 7.57 & 2.75 & 0.07 \\ Proposed model & 1.52 & 0.07 & 5.20 & 2.28 & 0.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The evaluation metrics of different methods. Figure 6: Fork price predictions based on four different methods. and 31.92% in the MSE and RMSE metrics, respectively. This indicates that the GRNN model achieved good predictive performance relative to the SVR and ELM models. (2) Analysis of the results of individual prediction models  
The PSO-SVR, PSO-GRNN, and PSO-ELM models manifested significantly enhanced predictive performance in contrast to their non-optimized equivalents, namely the SVR, GRNN, and ELM models, respectively. Particularly, the PSO-ELM model had RMSE and TIC values of 3.29 and 0.08 respectively. Compared with the PSO-SVR and PSO-GRNN models, the PSO-ELM model demonstrated a reduction in the RMSE value by 55.55% and 18.94%, respectively. When contrasted with the SVR model, the PSO-SVR presented reductions in both the MSE and RMSE by 27.41% and 14.80%, respectively. Particle swarm optimization (PSO) has been effectively utilized to finely adjust the parameters of SVR models, generating positive results [39]. Compared with the GRNN model, the PSO-GRNN model accomplished a decrease in MSE and RMSE by 10.76% and 5.54%, respectively. When pitted against the ELM model, the PSO-ELM model saw a more significant drop in MSE and RMSE by 72.83% and 47.88%, respectively. The combination of ensemble empirical modal decomposition (EEMD) and PSO for displacement prediction has been noted to surpass the accuracy of ELM and PSO-BPNN models [22]. The predictive capabilities of the SVR, GRNN, and ELM models were enhanced through PSO optimization of their parameters. The parameter  
Figure 7: Fork price predictions based on seven different methods. optimization of SVR, GRNN, and ELM was facilitated by PSO's robust global search capability and swift convergence [31; 40].