Nonlinear Grey Prediction Model with Convolution Integral NGMC (1,n) and Its Application to the Forecasting of China’s Industrial SO2 Emissions

The grey prediction model with convolution integral GMC (1, n) is a multiple grey model with exact solutions. To further improve prediction accuracy and describe better the relationship between cause and effect, we introduce nonlinear parameters into GMC (1, n) model and additionally apply a convolution integral to produce an improved forecasting model here designated as NGMC (1, n). The model solving process applied the least-squares method to evaluate the structure parameters of the model: convolution was used to obtain an exact solution with this improved grey model. The nonlinear optimisation took the parameters as the decision variables with the objective of minimising forecasting errors. The GMC (1, 2) and NGMC (1, 2) models were used to predict China’s industrial SO2 emissions from the basis of the economic output level as the influencing factor. Results indicated that NGMC (1, 2) can effectively describe the nonlinear relationship between China’s economic output and SO2 emissions with an improved accuracy over current GMC (1, 2) models.