An improved rolling NGBM(1,1) forecasting model with GRG nonlinear method of optimization for fossil carbon dioxide emissions in Malaysia and Singapore

This article analyzed and forecasted fossil carbon dioxide emissions in Malaysia and Singapore from year 2008 to 2016. Currently, there is a gap in this area of study in determining the most optimum value of ω and the value of index n in the generation of B matrix factor in Grey Model. This paper used the annual fossil carbon dioxide emissions in Malaysia and Singapore from 2008 to 2016. The study used the power form of Grey forecasting model called the Nonlinear Grey Bernoulli forecasting model (NGBM), with cooperation of Generalized Reduced Gradient (GRG) Nonlinear method of optimization. This study also applied the rolling mechanism to the NGBM model (RNGBM) which constructed a time varying sets of data when new observations arose, whereby the value ω and the value of index n used GRG Nonlinear method of optimization to produce a more accurate forecasting model. According to the forecasted result, it has been proven that the proposed RNGBM model with GRG Nonlinear method of optimization is able to produce a better precision of forecasting compared to the traditional RNGBM model. This article is able to give awareness to the public constitution and NGOs in creating a proper renewable energy modus operandi in lowering the carbon footprint to the environment, to overcome the major global warming issues