A novel fractional multivariate GM(1,N) model with interaction effects and its application in forecasting carbon emissions from China's civil aviation

Purpose The purpose is to forecasting carbon emissions from China's civil aviation more accurately, a novel fractional multivariate GM(1,N) model with interaction effects is developed in this paper. Design/methodology/approach First, the interaction term, the trend terms are introduced in the grey action term to reflect the influence of the interaction between the system-related variables on the change of the system characteristic variables and the time trend of the system development. Then fractional cumulative generating sequence is used as the modeling sequence to reduce the perturbation of the original data. Finally, in order to effectively find the optimal fraction accumulation generation coefficient, the particle swarm optimization (PSO) is used to determine the emerging coefficient. Findings Experimental results show that FIEGM(1, N) outperforms other grey prediction models in predicting the carbon emissions of CAAC, which can better solve the problem of multivariate system prediction of small samples with trend interaction effect. Originality/value By considering the influence of interactions in the system and the trend of system development in combination with fractional accumulation theory, a new method to improve the prediction performance of the GM(1, N) model is proposed. The model is first applied to the prediction of carbon emission of civil aviation in China.