An Ensemble Learning Method for the Kernel-Based Nonlinear Multivariate Grey Model and its Application in Forecasting Greenhouse Gas Emissions

The global warming problem caused by greenhouse gas (GHG) emissions has aroused wide public concern. In order to give policy makers more power to set the specific target of GHG emission reduction, we propose an ensemble learning method with the least squares boosting (LSBoost) algorithm for the kernel-based nonlinear multivariate grey model (KGM) (1, N), and it is abbreviated as BKGM (1, N). The KGM (1, N) has the ability to handle nonlinear small-sample time series prediction. However, the prediction accuracy of KGM (1, N) is affected to an extent by selecting the proper regularization parameter and the kernel parameter. In boosting scheme, the KGM (1, N) is used as a base learner, and the use of early stopping method avoids overfitting the training dataset. The empirical analysis of forecasting GHG emissions in 27 European countries for the period 2015–2019 is carried out. Overall error analysis indicators demonstrate that the BKGM (1, N) provides remarkable prediction performance compared with original KGM (1, N), support vector regression (SVR), and robust linear regression (RLR) in estimating GHG emissions.