To address the challenges of small sample size, strong nonlinearity, and multifactor coupling in predicting annual mean \({\text{P}}{{\text{M}}_{2.5}}\) concentrations in Tianjin, this study aims to provide a prediction method with high accuracy and robustness. To this end, the traditional multivariable grey prediction model is extended by incorporating the Euler polynomial, a linear correction term, and an autoregressive term, thereby enhancing its adaptability to complex sequences. Moreover, a differentiated combinatorial optimization of the accumulation order and background value coefficient for each variable is performed to further improve prediction accuracy. The proposed model is then applied to forecast the annual mean \({\text{P}}{{\text{M}}_{2.5}}\) concentration in Tianjin. The results show that its fitting and prediction accuracy are significantly superior to those of comparable grey models as well as mainstream statistical and machine learning methods. Based on this, the model forecasts a sustained improvement trend in Tianjin’s \({\text{P}}{{\text{M}}_{2.5}}\) concentration from 2024 to 2028 and identifies clear and stable dominant driving factors through sensitivity analysis. These results are then linked to the ecological and environmental targets of the 14th Five-Year Plan. Using the existing data, this study preliminarily assesses the likelihood of meeting those targets and the projected trends, while proposing initial management recommendations. The findings can serve as a valuable reference for optimizing regional air pollution prevention and control pathways as well as for corporate environmental risk management.
