## 4 Results
### Analysis of Long-Term Prediction Result  
In contrast to the foregoing short-term prediction task, long-term prediction is not so straightforward; it is often challenging to foresee what happens several days later. Next, we analyze the longer-term PM\({}_{2.5}\) concentration prediction performance of the model. The quantitative results of long-term PM\({}_{2.5}\) concentration prediction for the Beijing dataset are reported in Table 3, which provides a comparison of RMSE, MAE, R\({}^{2}\), and IA from classical deep learning models, hybrid deep learning models, and the FPHFA model. Table 3 shows the FPHFA model outperformed other prediction models in long-term PM\({}_{2.5}\) concentration prediction. Compared to other comparison models, the RMSE of FPHFA in the Beijing dataset is reduced to 22.12, MAE is reduced to 15.27, MAPE is reduced to  
Figure 9: Predictions 12 h ahead in experiments on the Beijing dataset. The graphs compare one month’s worth of actual and predicted PM\({}_{2.5}\) values (1 December 2016–31 December 2016) at station 1003A with different models. **(a)** LSTM; **(b)** GRU; **(c)** CNN-LSTM; **(d)** DAQFF; **(e)** FPHFA. 0.438, R2 is improved to 0.932, and IA is improved to 98.30%, which represents an obvious improvement in the accuracy of prediction. In addition, the error of the DAQFF model of hybrid deep learning models is inferior to that of the CNN-LSTM, but the difference between the two models is not large, and the error of both models is lower than that of the classical deep learning models. This implies that the hybrid deep learning approach is more suitable than the classical deep learning model for the task of predicting PM2.5 concentration prediction over the long term. Additionally, compared with the DAQFF model, FPHFA improved R2 by 0.068 and IA by 1.47% while reducing RMSE by 7.03 and MAE by 5.3. the results demonstrate that our FPHFA model performs better for both short-term and long-term prediction than DAQFF models. The impact of prediction size on FPHFA and other deep-learning models is then examined. Figure 10 shows that as the forward prediction size increases, the performance of the prediction for those models gradually decreases. It is important to note that the model performance evaluation indicators of traditional deep learning models are comparable to and occasionally even superior to those of CNN-LSTM when the prediction size is smaller than 60. Does this imply that CNN-LSTM's predicting performance is inferior to some traditional deep learning models? In fact, such is not generally the case, as Figure 10 also shows that the prediction performance of the hybrid deep learning models exceeds that of the classical deep learning models as the prediction horizon lengthens. Moreover, compared to models, the predicting performance of the LSTM, GRU, and CNN-LSTM models exhibits large fluctuations in long-term prediction at certain prediction horizons (e.g., 24-36 h, 72-84 h). The findings in Figure 10 are very noteworthy since they show that as the prediction size increases, FPHFA outperforms other models at any prediction time step (24-96 h) and is more stable. Moreover, we observe that compared with other models, FPHFA also has the lowest prediction error (RMSE and MAE) and the highest prediction accuracy (R2 and IA) at different prediction sizes. In order to verify the prediction performance of the model in different periods, we divided the data into four groups according to seasons and used the model to predict the pollutant data in different seasons. Tables 4 and 5 show the comparison of the five deep-learning models in different seasons. For the prediction of pollutant concentration in different seasons, the model we designed has achieved the optimal prediction results. In addition, it is obvious that the prediction accuracy of the model has some seasonal differences. In terms of reducing the prediction error and improving the consistency between the predicted data and the real data, the prediction results of the model in different seasons are not the same.