# Research on Agricultural Product Price Prediction Based on Improved PSO-GA
## 4 Results
### Forecast Analysis
#### 4.2.2 Prediction Results of Combined Models
In terms of direction prediction, on average, the semi-heterogeneous model improved the value of \(\text{D}_{\text{stat}}\) by 9.76% compared to the isomorphic model, while there was little change compared to the heterogeneous model. These findings reveal that by optimizing the combination weights, the semi-heterogeneous combination strategy can achieve better prediction. Even for models designed on the same dataset, the prediction performance can be significantly improved by introducing more diverse models. In order to further compare the prediction accuracies of different combination models, the MAPE values of the eight-seeded strategy under the three combination methods are compared. The results are shown in Table 9, below. The data show in Figures 7 and 8 that in most cases, the method of determining the weights of each model in the combination model by PSO-GA has the smallest error value for the MAPE compared with the mean and median methods. In addition, the MAPE values of the PSO-GA-based portfolio models decreased by an average of 14.09% compared to the mean-based benchmark portfolio model, and 11.20% compared to the median method. The PSO-GA of the full model was the most effective, with the lowest error and highest accuracy. Its MAPE value for large scallions is 1.9209%, which is a decrease of 8.96% compared to the MAPE value for the best single model, SSA-ARIMA. As shown in Table 9, among the homogeneous models, the ARIMA-based model performs better, and this result suggests that the combination of homogeneous models with different decomposition techniques can further improve prediction accuracy. Among the heterogeneous models, the SSA-based model performs the best, with the smallest MAPE error, and its prediction performance is quite excellent compared with the single model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Decomposition Method** & **RMSE** & **MAE** & **MAPE (\%)** & \(\text{D}_{\text{stat}}\) \\ \hline \multirow{4}{*}{ARIMA} & single & 0.1536 & 0.1133 & 3.7684 & 0.4174 \\  & SSA & 0.0871 & 0.0635 & 2.1098 & 0.6355 \\  & EMD & 0.0920 & 0.0697 & 2.3758 & 0.6449 \\  & VMD & 0.1327 & 0.0961 & 3.2247 & 0.6531 \\ \hline \multirow{4}{*}{LSTM} & single & 0.1675 & 0.1211 & 4.0358 & 0.4399 \\  & SSA & 0.0906 & 0.0666 & 2.2651 & 0.7753 \\  & EMD & 0.1433 & 0.1018 & 3.2626 & 0.6013 \\  & VMD & 0.1072 & 0.0790 & 2.6165 & 0.5175 \\ \hline \multirow{4}{*}{GRUs} & single & 0.1513 & 0.1122 & 3.8860 & 0.4272 \\  & SSA & 0.0959 & 0.0708 & 2.4120 & 0.6266 \\ \cline{1-1}  & EMD & 0.1125 & 0.0859 & 3.0221 & 0.6519 \\ \cline{1-1}  & VMD & 0.1498 & 0.1100 & 3.7797 & 0.5016 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Evaluation of denoising hybrid strategies for scallion prices. \begin{table}
\begin{tabular}{c c c c c} \hline  & **RMSE** & **MAE** & **MAPE** & **Dstat** \\ \hline Mean & 0.1213 & 0.0896 & 0.0304 & 0.5683 \\ \hline Median & 0.1170 & 0.0866 & 0.0294 & 0.5848 \\ \hline PSO-GA & 0.1046 & 0.0776 & 0.0261 & 0.6362 \\ \hline \end{tabular}
\end{table} 
Table 6: PSO-GA, mean, median comparison of three methods in four indicators. \begin{table}
\begin{tabular}{c c c} \hline \multicolumn{2}{c}{**Combination Strategy**} & \multicolumn{2}{c}{**Individual Models**} \\ \hline Panel A: Homogeneous & & \\ ARIMA-based & ARIMA, EMD-ARIMA, VMD-ARIMA, SSA-ARIMA \\ LSTM-based & LSTM, EMD-LSTM, VMD-LSTM, SSA-LSTM \\ GRU-based & grus, emd-grus, vmd-grus, ssa-grus \\ \hline Panel B: Heterogeneous & & \\ SSA-based & SSA-ARIMA, SSA-LSTM, SSA-GRUs \\ VMD-based & vmd-arima, vmd-lstm, vmd-grus \\ EMD-based & EMD-ARIMS, EMD-LSTM, EMD-GRUs \\ \hline Panel C: Semi-heterogeneous & & \\ Full-based & ssa-arima, ssa-lstm, ssa-grus, vmd-arima, vmd-lstm, vmd-grus, emd-arims, \\ emd-lstm, emd-grus & & \\ \hline Panel D: Benchmark combination model & & \\ Single-based & ARIMA, LSTM, GRUs \\ \hline \end{tabular}
\end{table} 
Table 7: The individual models for different combination strategies.