## 4 Experimental Results and Analysis
### Time Series Trend Analysis
The above mentioned trend of PM\({}_{2.5}\) concentration in 2012-2022 has a multifaceted effect on the prediction of each model in 2023. According to Figure 8 (monthly average PM\({}_{2.5}\) concentration line chart of each model in 2023), each model refers to the trend characteristics of historical data (the main characteristics used in this experiment) and the seasonal fluctuations caused by various factors when predicting the concentration of 2023. The LightGBM model, with its excellent nonlinear fitting ability, effectively captures the complex changes in the historical trends from 2012 to 2022, and applies it to the PM\({}_{2.5}\) concentration forecast for 2023. From the trend of the line chart, we can see that the model can more accurately grasp the overall trend of high concentration at the beginning of the year (such as the actual concentration in January is about 41 \(\mu\)g/m\({}^{3}\), and the LightGBM model predicts a value of about 58 \(\mu\)g/m\({}^{3}\)), then declines, and rebounds at the end of the year (the actual concentration in December is about 33 \(\mu\)g/m\({}^{3}\), and the predicted value is about 52 \(\mu\)g/m\({}^{3}\)). This is due to its effective learning of seasonal changes, holiday  
Figure 8: Monthly Average PM\({}_{2.5}\) concentration in 2023 by Model. impacts, and special fluctuations during the epidemic in historical data. However, from the comparison between the overall forecast results and the actual values, the predicted values of the model are generally higher than the actual values, and there is a significant \"overestimation\" phenomenon. This shows that although the model can learn historical influencing factors, it does not take into account the changes in new pollution sources, differences in meteorological conditions, and different holiday activities in 2023, and further optimization is needed to improve the accuracy of the forecast. The Prophet model has certain methods for dealing with seasonality, trend and holiday effects of time series. However, when predicting the concentration in 2023 based on the trend from 2012 to 2022, the performance is not satisfactory. In the stage of concentration decline, the predicted value of the model deviates greatly from the original data, showing an obvious \"underestimation\" trend. For example, during the period from April to July, the actual concentration dropped from about 32 ug/m\({}^{3}\) to about 15 ug/m\({}^{3}\), while the predicted value of the Prophet model was always lower than the actual value, and the gap gradually increased. This may be because the Prophet model simply models the holiday effect and seasonal changes when processing historical data, ignoring the significant differences in pollution sources and meteorological conditions between 2023 and previous years. For example, in 2023, some factories upgraded their emission reduction equipment and reduced pollutant emissions, but the model did not take this key change into account. When using the previous average diffusion coefficient for prediction, the prediction of the concentration decline stage was seriously underestimated. As a classic time series model, the SARIMA model builds a model based on the data characteristics from 2012 to 2022 to predict the concentration in 2023. In some months, it can reflect the trend of concentration changes, but there are deviations from the actual values in the overall seasonal fluctuation range and the prediction of some key time points. Nevertheless, compared with the other two models, its deviation is relatively small. For example, in September and November, there is a certain difference between the actual concentration and the predicted value. This may be because the model has high requirements for the stability of the data, and the concentration changes in 2023 are affected by the combined effect of multiple factors such as the resumption of normal holiday activities and the gradual weakening of the impact of the epidemic. It does not fully conform to the stable pattern presented by historical data.