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Journal of Applied Mathematics
Volume 2014, Article ID 580161, 9 pages
Research Article

Nonlinear Grey Prediction Model with Convolution Integral NGMC and Its Application to the Forecasting of China’s Industrial Emissions

1School of Economics & International Trade, Zhejiang University of Finance & Economics, Hangzhou, Zhejiang 310018, China
2College of Economics & Management, Nanjing University of Aeronautics & Astronautics, Nanjing, Jiangsu 210016, China

Received 11 December 2013; Accepted 14 February 2014; Published 24 March 2014

Academic Editor: Hui-Shen Shen

Copyright © 2014 Zheng-Xin Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.