A novel fractional-order grey prediction model: a case study of Chinese carbon emissions

Objective and accurate prediction of carbon emissions can provide a basis for the country to achieve carbon emission reduction targets and can also comprehensively and scientifically predict the peak of carbon emissions effectively, providing valuable reference information for the implementation of specific emission reduction policies and measures at each stage. In this paper, a novel fractional-order grey multivariate forecasting model is established to analyze and forecast China's carbon emissions, reflecting the principle of new information priority. The model adds fractional-order cumulative sequences to the traditional integer-order cumulative sequences, uses the Gamma function to represent the fractional-order sequences and the time-response equation, and uses the particle swarm algorithm to find the optimal order of the cumulative sequence. Finally, the modeling steps of the model are given. Then, the new model is analyzed for its effectiveness from three different perspectives using 21 years of Chinese carbon emission data. The results of the first and second cases show that the newly established particle swarm optimization fractional-order model is superior to the grey multivariate comparison model. The results of the third case show that the new model is superior to the three classical grey prediction comparison models. It has stable characteristics for both simulation and prediction and also shows high accuracy, and all three cases fully illustrate the effectiveness of the new model. Finally, this new model is applied to forecast China's carbon emissions from 2022-2026, analyze the forecast results, and make relevant recommendations.