Fractional Grey Breakpoint Model for Forecasting PM2.5 Under Energy Policy Shock

Traditional fossil fuel consumption is the main contributor increased atmospheric PM2.5 concentration. In 2014, China designated 81 new-energy demonstration cities, aiming to replace traditional fossil fuel energy with renewable energy. This research aimed to forecast PM2.5 trends. Fractional policy shock term was introduced into grey model to simulate the temporal variability. This model was compared with several existing models to confirm its accuracy and efficacy. We also assessed the robustness characteristics of key parameter. This research found the following: (1) The new-energy demonstration policy achieved stable PM2.5 reductions in the Beijing-Tianjin-Hebei agglomeration. The policy showed strong regional linkages and marginal mitigation effects. (2) The fractional breakpoint grey model (FBGM(s,t)) outperformed existing classical forecasting models and neural networks in fitting and generalization capability. FBGM(s,t) decreased the MAPE by over 2% across all four cities. (3) Robustness analyzes confirmed that the model’s performance advantage remained stable under reasonable parameter variations.