A novel multi-fractional multivariate grey model for city air quality index prediction in China

With the continuous development of science and technology, the problem of air pollution is increasingly serious. The Air Quality Index (AQI) serves as an effective indicator of air quality variations. Scientific forecasting of AQI plays a significant role in addressing this issue. Aiming at the small monthly data of city AQI, a multi-fractional multivariate grey model is proposed,which based on GMC (1, n) model. Firstly, the model proposes a multi-fractional cumulative generator, that is, an independent fractional cumulative generator is defined for each variable. Additionally, the Moth-Flame Optimization (MFO) is selected to optimize the nonlinear parameters. To demonstrate the model's performance, numerical examples and real-world AQI data from four Chinese cities, namely Nanjing, Beijing, Hangzhou and Lhasa , are used to construct the forecasting model. A comparative analysis is conducted against six existing grey models, multiple linear regression model and BPNN neural network. The results indicate that the proposed model consistently outperforms the other models in terms of prediction accuracy and reliability.