Hybrid framework combining grey system model with Gaussian process and STL for CO2 emissions forecasting in developed countries

Accurate forecasting of carbon dioxide (CO2) emissions is crucial for achieving carbon neutrality early, as CO2 is the primary component of greenhouse gases. The time series of CO2 emissions exhibit obvious trends and seasonal characteristics affected by energy consumption and climate. A hybrid forecasting framework combining the grey system model with Gaussian process residual uncertainty analysis and Seasonal -Trend decomposition using LOESS (STL) is proposed to capture these characteristics efficiently. The time series is systemically decomposed into trends, seasonal, and residual by the STL. The grey system models are utilized for constructing the trends forecasting scheme. Meanwhile, residual uncertainty analysis is executed by Gaussian Process Regression (GPR) using a multi -step ahead rolling forecasting strategy designed for univariate time series. Additionally, the salp swarm algorithm is utilized to tune the nonlinear parameters of the proposed models. The proposed framework is applied in the EU27 & UK, Japan, Russia, and the US, compared with machine learning models, grey system models, and the hybrid model with another decomposition method with multiple evaluation metrics (including 13 metrics). The results demonstrate that the hybrid model based on adjacent non -homogeneous discrete grey model (ANDGM) and GPR (ANDGM-GPR) holds the best performance among all the models. Meanwhile, most proposed models outperform other kinds of models. The ANDGM-GPR offers the smallest MAPE of 2.7611%, while the MAPEs of GPR and ANDGM are 7.8377% and 11.2495%, respectively, in the same case. Thus, the proposed method has a high potential for forecasting CO2 emissions, as it performs well in actual cases.