# Research on Agricultural Product Price Prediction Based on Improved PSO-GA
## 4 Results
### Forecast Analysis
#### 4.2.2 Prediction Results of Combined Models  
This subsection demonstrates the prediction performance of the combination model by comparing the prediction effect of the combination model, as well as the performance of the combination methods, by using three combination methods for different combinations of models, which include the mean (MEAN), median (MED), and PSO-GA methods. First, Table 6, below, demonstrates the average prediction performance of the three prediction combination methods. The data show that all three combination methods contribute to obtaining better prediction results and have a stable prediction ability. In the linear combination methods (the average method and median method), they determine the weights of each of the combination models by statistical methods, and the MED method performs better than the average method in most cases, but it does not consider the performance differences between different models within the combination, and ignores the prediction bias between the models. In contrast, among the intelligent optimized combination methods, PSO-GA improves the stability and accuracy of the overall prediction by taking advantage of the complementarity between models, thus clearly overcoming the limitations of the linear combination methods. As can be seen in Figure 6, the PSO-GA method has, on average, the lowest values for RMSE, MAE, MAPE, and the highest value for Dstat, compared to the mean and median methods. Compared to the mean method, PSO-GA has 13.77%, 13.37%, and 14.09% lower RMSE, MAE, and MAPE, respectively, and 10.67% higher directional accuracy Dstat. Compared with the median method, the RMSE, MAE, and MAPE of PSO-GA were reduced by 10.65%, 10.35%, and 11.20%, respectively, and the directional accuracy Dstat was improved by 8.07%. This indicates that the PSO-GA method can make full use of the complementarity between the prediction results of different single models to find the global optimal solution through powerful global search and optimization capabilities, thus improving the accuracy of the prediction results, and it also effectively proves the robustness of the combined PSO-GA method in predicting the price of large scallions. Secondly, different combinations are divided into different combination strategies due to different decomposition techniques and prediction models, which makes the prediction performance of each combination strategy different. According to the similarity in the base model structure and the difference in the algorithm, the combination model is divided into  
Figure 6: PSO-GA, Mean, and Median comparison of three methods in four indicators. three combination strategies: isomorphism, heteromorphism, and semi-heteromorphism. Their base models in the combination model under the different combination strategies are shown in Table 7, and their prediction performance is shown in Table 8, below. From the data, we can see that all three combination strategies can significantly improve the prediction performance. In terms of the prediction accuracy measured by the RMSE, MAE, and MAPE, the homogeneous model reduces by, on average, 24.26%, 23.82%, and 23.73% compared to the single combination model without decomposition, and the heterogeneous model reduces by, on average, 31.03%, 30.66%, and 29.73% compared to the single combination model. In terms of directional accuracy, the \(\text{D}_{\text{stat}}\) of the homogeneous (heterogeneous) model increased by an average of 27.00% (34.72%). The semi-heterogeneous combination strategy (i.e., all-base combination) benefits significantly from model diversity compared to one of the other two combination strategies, and collectively tends to produce the best predictions, with the lowest horizontal accuracy and highest directional accuracy. In terms of prediction accuracy, the semi-heterogeneous models reduced each metric by 17.43%, 17.14%, and 16.32% on average compared to the homogeneous models and by 9.32%, 8.97%, and 9.18% on average compared to the heterogeneous models.