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PurposePM10 is one of the most dangerous air pollutants which is harmful to the ecological system and human health. Accurate forecasting of PM10 concentration makes it easier for the government to make efficient decisions and policies. However, the PM10 concentration, particularly, the emerging short-term concentration has high uncertainties as it is often impacted by many factors and also time varying. Above all, a new methodology which can overcome such difficulties is needed.Design/methodology/approachThe grey system theory is used to build the short-term PM10 forecasting model. The Euler polynomial is used as a driving term of the proposed grey model, and then the convolutional solution is applied to make the new model computationally feasible. The grey wolf optimizer is used to select the optimal nonlinear parameters of the proposed model.FindingsThe introduction of the Euler polynomial makes the new model more flexible and more general as it can yield several other conventional grey models under certain conditions. The new model presents significantly higher performance, is more accurate and also more stable, than the six existing grey models in three real-world cases and the case of short-term PM10 forecasting in Tianjin China.Practical implicationsWith high performance in the real-world case in Tianjin China, the proposed model appears to have high potential to accurately forecast the PM10 concentration in big cities of China. Therefore, it can be considered as a decision-making support tool in the near future.Originality/valueThis is the first work introducing the Euler polynomial to the grey system models, and a more general formulation of existing grey models is also obtained. The modelling pattern used in this paper can be used as an example for building other similar nonlinear grey models. The practical example of short-term PM10 forecasting in Tianjin China is also presented for the first time.

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