Modelling the nonlinear relationship between CO2 emissions and economic growth using a PSO algorithm-based grey Verhulst model

A new method for discussing the relationship between CO2 emissions and economic growth is proposed using grey systems theory. GDP and CO2 emissions per capita are separately regarded as the input to, and output of, a grey system to establish a non-equigap grey Verhulst model (NE grey Verhulst model). To avoid the errors resulting from substituting a difference equation for a differential equation in grey modelling theory, the derived non-equigap grey Verhulst model (DNE grey Verhulst model) is deduced. Moreover, the structural parameters of the model are optimised using a particle swarm optimisation (PSO) algorithm in an attempt to further improve modelling accuracy. Based on data relating to CO2 emissions and GDP per capita in China from 1990 to 2014, empirical research is conducted which shows that the relationship between CO2 emissions and economic growth exhibits an inverted U-shape and the emissions are in a rapid growth stage on the left of the curve. It is predicted that CO2 emissions per capita will continue to rise from 2016 to 2020 and will not reach their peak before 2030, so the Chinese government should take effective measures to reduce carbon emissions.