## 5 Discussion  
### Model Selection Rationale  
Before we delve into the performance of the models, it is necessary to explain why we chose the three models of SARIMA, Prophet and LightGBM to predict PM\({}_{2.5}\) concentration in Nanning urban area. Accurate prediction of PM\({}_{2.5}\) concentration is extremely important for urban environmental management and public health protection, and appropriate model selection is the key to achieving accurate prediction. Our study aims to comprehensively evaluate the performance of different types of models in predicting PM\({}_{2.5}\) concentration in Nanning urban area, and provide a scientific basis for subsequent research and practical applications. The PM\({}_{2.5}\) concentration in Nanning urban area is affected by many factors such as meteorological conditions, human activities, and topography. The interaction of these factors causes the concentration change to present a complex situation, which not only shows obvious seasonal and trend characteristics, but also has complex nonlinear relationships. In addition, the research data has time series characteristics and covers information at different time resolutions. Based on these research objectives and data characteristics, we selected the following three models:  
As a mature statistical time series analysis tool, the SARIMA model has a deep theoretical foundation and extensive application practice in processing data with seasonality and trend. The PM\({}_{2.5}\) concentration data in Nanning urban area shows a significant seasonal variation pattern. For example, in summer, precipitation is relatively abundant, which has a flushing effect on pollutants and the concentration is relatively low. In winter, the atmospheric diffusion conditions are relatively poor, and pollutants are easy to accumulate, making the PM\({}_{2.5}\) concentration relatively high. In the long run, with the development of the city and the implementation of environmental protection policies, the PM\({}_{2.5}\) concentration also shows a specific trend of change. The SARIMA model can effectively capture the seasonal and trend characteristics in the data through autoregression (AR), difference (I) and moving average (MA) components. The reasonable setting of its non-seasonal parameters (p, d, q) and seasonal parameters (P, D, Q, S) helps to accurately model the time series of PM\({}_{2.5}\) concentration in Nanning urban area. In this study, the non-seasonal parameters are set to non_seasonal_order = (1, 1, 1), the seasonal parameters are set to seasonal_order = (1, 1, 1), and S = 12. This setting enables the model to fully consider the seasonal fluctuations of PM\({}_{2.5}\) concentration on a monthly scale and the long-term trend of the data. By learning from historical data, the SARIMA model can dig out potential patterns and provide a reliable basis for predicting future changes in PM\({}_{2.5}\) concentration. Therefore, choosing the SARIMA model helps analyze the long-term trend of PM\({}_{2.5}\) concentration in Nanning urban area and provides strong support for long-term monitoring and prediction of air quality. The Prophet model was developed by Facebook and is a time series prediction tool specifically for processing data containing seasonal and holiday effects. The PM\({}_{2.5}\) concentration in Nanning urban area is not only affected by seasonal changes, but also significantly changes due to changes in human activities during holidays. For example, during the National Day holiday, changes in traffic flow and residents' activity patterns will lead to an increase in PM\({}_{2.5}\) emissions, which in turn affects the concentration level. The additive model structure of the Prophet model, y (t) = g (t) + s (t) + h (t), enables it to model trends (g (t)), seasonality (s (t)), and holiday effects (h (t)) respectively. The model can automatically identify and fit seasonal patterns in the data without pre-setting complex seasonal parameters.