## 5 Conclusions  
The data regarding agricultural prices in wholesale markets possess characteristics of nonlinearity and cyclicality, making the accurate prediction of these prices essential for producers to adjust their production plans and guarantee the stability of agricultural market prices. To overcome the limitations of individual forecasting models in capturing all the subtleties of agricultural price series and their frequently insufficient forecasting accuracy, this study introduces a prediction approach that depends on combined residual correction. This research presents two major innovations. Firstly, the input weights and hidden layer biases of the ELM model are assigned randomly, and these assignments can affect the model's convergence speed and accuracy. In the proposed method, the SSA is utilized to optimize the weights and thresholds of the ELM model, thereby enhancing its generalization ability and predictive accuracy. Secondly, the penalty factors and kernel function parameters have a significant influence on the predictive performance of the SVR model. In the proposed method, the SSA is employed to optimize these parameters for the SVR, with the aim of enhancing its generalization ability and prediction accuracy. Finally, considering that the prediction accuracy of a single model can fluctuate over time, with periods of high and low accuracy, this study introduces the use of the IOWA operator. This operator combines the predicted residuals' weights from the SSA-SVR and SSA-ELM models to calculate the combined residual prediction value at each point in the sample interval, further improving the forecast results of the GRNN model. To assess the effectiveness of the models, monthly pork price data from Beijing spanning January 2009 to September 2024 were selected for analysis. A comparative study was conducted on the predictive performance of nine models: SVR, GRNN, ELM, PSO-SVR, PSO-GRNN, PSO-ELM, SSA-SVR, SSA-GRNN, and SSA-ELM. The findings revealed that the PSO-SVR, PSO-GRNN, and PSO-ELM models achieved higher predictive accuracy compared to the standard SVR, GRNN, and ELM models, respectively. In a similar vein, the SSA-SVR, SSA-GRNN, and SSA-ELM models also demonstrated improved predictive accuracy over the standard SVR, GRNN, and ELM models, respectively. This indicated that both PSO and SSA are capable of effectively tuning the parameters of the SVR, GRNN, and ELM models, thereby enhancing their predictive accuracy. In order to verify the validity of the models, data on the monthly pork price in Beijing from January 2009 to September 2024 were chosen, and the forecasting effects of nine models, namely the SVR, GRNN, ELM, PSO-SVR, PSO-GRNN, PSO-ELM, SSA-SVR, SSA-GRNN, and SSA-ELM models, were compared. The results indicated that the prediction accuracies of the PSO-SVR, PSO-GRNN, and PSO-ELM models were, respectively, higher than those of the SVR, GRNN, and ELM models. Moreover, the prediction accuracies of the SSA-SVR, SSA-GRNN, and SSA-ELM models were higher than those of the SVR, GRNN, and ELM models, respectively. It was demonstrated that PSO and the SSA can effectively optimize the parameters of the SVR, GRNN, and ELM models and improve the \begin{table}
\begin{tabular}{c c c c} \hline
**Month** & **Forecasted Value (CNY/kg)** & **Month** & **Forecasted Value (CNY/kg)** \\ \hline
2024M10 & 21.37 & 2025M06 & 17.95 \\
2024M11 & 21.49 & 2025M07 & 17.39 \\
2024M12 & 22.07 & 2025M08 & 18.55 \\
2025M01 & 19.81 & 2025M09 & 20.04 \\
2025M02 & 18.13 & 2025M10 & 17.37 \\
2025M03 & 19.39 & 2025M11 & 17.11 \\
2025M04 & 18.20 & 2025M12 & 16.84 \\
2025M05 & 17.92 & & \\ \hline \end{tabular}
\end{table} 
Table 4: The pork price forecasts for the next nine periods. model prediction accuracy. Compared with the SVR, GRNN, ELM, PSO-SVR, PSO-GRNN, PSO-ELM, SSA-SVR, SSA-GRNN, and SSA-ELM models, the proposed model exhibited variable degrees of decrease in the MAE, MAPE, MSE, RMSE, and TIC values.