Enhancing Quarterly Carbon Emission Forecasting in China：A small sample decomposition model based Caputo fractional derivative grey Riccati model and LSSVR

Abstract

Abstract Accurately predicting carbon emissions is a crucial scientific foundation for the monitoring and evaluation of a country's progress in achieving its intended carbon reduction goals. Given the constraints of a small sample size, the nonlinearity, and the complexity inherent in quarterly data on carbon emissions at the industrial level, this paper introduces the Caputo fractional derivative into the grey Riccati model, establishing a Caputo fractional derivative grey Riccati model with memory characteristics. The numerical solution of the model is acquired through the fractional Adams-Bashforth-Moulton predictor-corrector algorithm, with the model's parameters optimized using the grey Wolf optimization algorithm. Subsequently, the Caputo fractional derivative grey Riccati model is integrated with the EEMD decomposition algorithm and the least square support vector regression to construct a decomposition-integration model for carbon emission decomposition. Finally, the proposed decomposition-integrationmodel is validated using quarterly carbon emission data from six industries in China as an illustrative example. The results convincingly demonstrate that the proposed decomposition-integration prediction model effectively analyzes the developmental trajectory of industrial carbon emissions in China. Moreover, it exhibits superior stability and accuracy in both fitting and forecasting when compared to other integrated and single models.