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This paper presents GM (1, N) models with linear cross effect and nonlinear cross effect, and discusses the difference of driving factors between these two types of models to solve the cross effects of GM (1, N) model. The model with a linear cross effect in this paper preserves the solution of whitenization in the GM (1, 1) model. While the model with nonlinear cross effect integrates the sequences of systemic features, driving factors, and the cross effect of these driving factors. While applying support vector machine (SVM) regression, it transfers the nonlinear relationship among these sequences to a linear relationship. To test the GM (1, N) model that is based on support vector machine (SVM) with nonlinear effect, the study applies it to forecast the total output of the pharmaceutical industry. The range of the data is selected from 2005–2017, which the data from 2005–2013 are used to fit into the model. The GM (1, N) model based on SVM with nonlinear cross effect achieves 0.6566 and 0.2956 in its fitted total of relative error and the forecast total of relative error, respectively. The new model presents a more accurate analysis on fitting and forecast precision than the classic GM (1, N) model and GM (1, N) with the linear cross effect model.

An Improvement of GM (1, N) Model Based on Support Vector Machine Regression with Nonlinear Cross Effects