A novel robust reweighted multivariate grey model for forecasting the greenhouse gas emissions

In this paper, in order to accurately forecast the greenhouse gas (GHG) emissions at a national level, we propose a novel robust reweighted multivariate grey model, abbreviated as the RWGM(1,N), that reduces the potential for overfitting and performs more robust against outliers. The methodology starts from the un-weighted regularized multivariate grey model, abbreviated as the RGM(1,N), that treats the size of the coefficients and a penalty for the residuals as the objective function. To further distinguish the amount of shrinkage, the weighting factors are introduced and updated iteratively based on the previous errors until the convergence is realized or the maximum iterations is reached. As a result, the RWGM(1,N) does not increase the computational burden significantly, but it provides robust method for estimating the coefficients of multivariate grey model. In applications, the least absolute shrinkage and selection operator (LASSO) regression is employed to implement the variable selection for socioeconomic, energy-related and environment-related potential predictor variables, and the proposed model is utilized to simulate the GHG emissions in European Union (EU) member countries from 2010 to 2016. The results show that this novel model demonstrates a higher predicted accuracy and more robust performance over the other models considered for comparison.