Non-equidistant grey model with dynamic fractional order optimization: High precision carbon emission prediction for carbon neutrality

The fractional order accumulation calculation process in traditional grey system theory is too complex and has poor effectiveness in predicting carbon dioxide emissions in practical applications. A new non-equidistant grey model is proposed to address the above issues, which introduces a C-type fractional order cumulative derivative to simplify the calculation of fractional order accumulation. At the same time, introducing a dynamic fractional order adjustment strategy can adaptively optimize the fractional order value based on data characteristics, enhancing the flexibility and accuracy of the model in predicting carbon dioxide emissions. Thus, the C-type fractional order cumulative non-uniform grey model (1,1) is obtained. The research results show that compared with existing advanced non-equidistant GM (1,1) models based on integration, non-equidistant grey prediction models based on residual correction, and hybrid multi-scale machine learning models, the research method achieves higher accuracy while maintaining high computational efficiency. Its average absolute percentage error in performance testing is the lowest at only 1.987%, significantly better than other models. In practical applications, the research method has an average absolute percentage error of less than 10% in both foreign and domestic data prediction. Overall, this model can be applied in practical prediction of carbon dioxide emissions and provide data reference for achieving the goal of “carbon neutrality.”