## 6 Conclusions and Outlook  
Our study systematically evaluated the performance of three models, SARIMA, Prophet and LightGBM, in predicting PM\({}_{2.5}\) concentration in Nanning city in 2023. The study found that each model has its own advantages and limitations: SARIMA is good at capturing time series changes and is suitable for long-term monitoring, but has poor adaptability to non-stationary data. Prophet can handle the seasonality of time series and the impact of special events, but has weak prediction ability under extreme events and is prone to underestimate at high concentrations. LightGBM has strong feature extraction capabilities and can mine complex nonlinear relationships, but is prone to overfitting and has poor stability. In terms of spatial prediction, LightGBM can roughly divide high-concentration areas, but the details are not accurate enough. Prophet's spatial positioning is inaccurate, and the predicted values in some areas are low. SARIMA can show the overall trend, but the spatial characteristics of some areas are not captured enough. In the time dimension, LightGBM has a large prediction error in winter, Prophet performs poorly from May to July, and SARIMA is limited by data stability. The prediction performance decreases in January, May, September and November, but the overall deviation is relatively small. In addition, the error distribution of the three models is non-normal, indicating that there are limitations in processing PM\({}_{2.5}\) concentration data and further optimization is needed.  
In the future, our research will focus on improving the prediction level of PM\({}_{2.5}\) concentration and expanding the depth and breadth of research. Specifically, it includes: using genetic algorithms, particle swarm optimization algorithms, etc. to automatically adjust model parameters, optimize model structure, explore the integration of models such as SARIMA, Prophet, LightGBM and neural networks, integrate the advantages of each model, and build a real-time air quality prediction system that integrates multi-source data such as ground monitoring, satellite remote sensing, transportation, and industry. Further explore the depth of meteorological data, carry out PM\({}_{2.5}\) chemical composition prediction experiments, establish its quantitative relationship with related factors, establish a high-resolution model based on regional characteristics, consider the interaction of multi-scale factors, and use GIS technology to visualize the prediction results to help urban planning and environmental management decisions.  
Conceptualization: B.L., M.L. and N.Y.; Methodology: B.L. and M.C.; Software: B.L. and M.C.; Formal analysis: B.L. and M.C.; Investigation: B.L. and M.C.; Resources: B.L. and M.L.; Data curation: B.L. and N.Y.; Writing--Original Draft Preparation: B.L. and M.L.; Writing --Review and Editing: B.L. and M.C.; Visualization: B.L.; Supervision: N.Y. and M.C.; Project Administration: B.L. and N.Y.; Funding Acquisition: B.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Guangxi Zhuang Autonomous Region Human Resources and Social Security Department 2024 Young Scientist Program Scientific Research Start-up Fund (No. 60203038919630213), The key research development project of Guangxi (GK: AB22080101), Guangxi Innovation and Entrepreneurship Training Program for College Students (S202410603072), Nanning Normal University Doctoral Research Startup Project (No. 602021239447).  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author(s).  
During the preparation of this manuscript, the authors used [Doubao, 1.42.6_win] for the purposes of [polishing the introduction and discussion sections as well as checking the grammar of the entire text]. The authors have reviewed and edited the output and take full responsibility for the content of this publication.  
The authors declare no conflicts of interest.