## 4 Results and Discussion
### Combined Prediction Model Weighting Vector Determination  
As shown in Table 1, the mean accuracies for the SVR, ELM, SSA-SVR, and SSA-ELM models were 0.12, 0.44, 0.53, and 0.65, respectively. The SSA-optimized models (SSA-SVR and SSA-ELM) outperformed the original SVR and ELM models in terms of average precision. Specifically, the SSA-ELM model achieved the highest mean residual accuracy in pork price forecasting, while the SVR and ELM models had relatively lower accuracy.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Month**} & \multirow{3}{*}{
\begin{tabular}{c} **Residual Actual Value** \\ **Pork Price (CNY /kg)** \\ \end{tabular} } & \multicolumn{6}{c}{**Residual Prediction Value**} & \multicolumn{6}{c}{**Prediction Accuracy**} \\ \cline{3-10}  & & **SVR** & **ELM** & **SSA-SVR** & **SSA-ELM** & **SVR** & **ELM** & **SSA-SVR** & **SSA-ELM** \\ \hline
2021M07 & \(-\)2.44 & 0.14 & \(-\)2.08 & \(  
Table 2 provides details of the evaluation metrics for the residual predictions of each model. The SSA-SVR and SSA-ELM models both achieved higher residual prediction accuracy than their non-SSA counterparts. For the SSA-SVR model, the MAE, MAPE, MSE, RMSE, and TIC values were 1.88, 1.53, 9.87, 3.14, and 0.51, respectively. Compared with the SVR model, the RMSE of the SSA-SVR model decreased by 19.29%. For the SSA-ELM model, these values were 0.63, 1.93, 0.60, 0.77, and 0.09, respectively. Compared to the ELM model, the RMSE of the SSA-ELM model was reduced by 56.10%. These results underscore the importance of parameter tuning in forecasting model development and confirm that SSA significantly enhances the predictive accuracy of both SVR and ELM models.  
Due to the superior predictive accuracy of the SSA-SVR and SSA-ELM models compared to the traditional SVR and ELM models, these optimized models were chosen to undertake the ensemble prediction of the residuals from the GRNN model. The combined forecast using the IOWA method was determined according to Equation (7). The detailed calculation procedure is as follows.  
\[f_{L}(\langle a_{1,1},x_{11}\rangle,\langle a_{21},x_{21}\rangle)=f_{L}(\langle 0.99,-2.45\rangle,\langle 0.64,-3.31\rangle)=-2.45l_{1}-3.31l_{2} \tag{17}\]  
\[f_{L}(\langle a_{1,2},x_{1,2}\rangle,\langle a_{2,2},x_{2,2}\rangle)=f_{L}( \langle 0.74,-2.23\rangle,\langle 0.91,-2.72\rangle)=-2.23l_{2}-2.72l_{1} \tag{18}\]  
\[f_{L}(\langle a_{1,38},x_{1,38}\rangle,\langle a_{2,38},x_{2,38}\rangle)=f_{L} (\langle 0.41,2.34\rangle,\langle 0.91,5.11\rangle)=2.34l_{2}+5.11l_{1} \tag{19}\]  
\[f_{L}(\langle a_{1,39},x_{1,39}\rangle,\langle a_{2,39},x_{2,39}\rangle)=f_{L} (\langle 0.54,2.23\rangle,\langle 0.92,4.43\rangle)=2.23l_{2}+4.43l_{1} \tag{20}\]  
By substituting these equations into Equation (8), the optimal model under the minimum error sum of squares criterion can be obtained as follows.  
\[\begin{split}\min S(l_{1},l_{2})=\sum\limits_{t=1}^{39}\left[x_{ t}-f_{L}(\langle a_{1,t},x_{1,t}\rangle,\langle a_{2,t},x_{2,t}\rangle) \right]^{2}\\ s.t.\begin{cases}l_{1}+l_{2}=1\\ l_{1}\geq 0,l_{2}\geq 0\end{cases}\end{split} \tag{21}\]  
where \(x_{t}(t=1,2,\ldots,39)\) is the residual data of the pork price series, and the optimal weight coefficients \(l_{1},\ l_{2}\) are obtained by using the planning solution. The optimal weight coefficients of the IOWA-based optimal neural network residual correction prediction model were calculated as \(l_{1}=0.307,\ l_{2}=0.693\).