This paper presents GM (1, N) models with linear cross effect and nonlinear cross effect,\nand discusses the difference of driving factors between these two types of models to solve the cross\neffects of GM (1, N) model. The model with a linear cross effect in this paper preserves the solution\nof whitenization in the GM (1, 1) model. While the model with nonlinear cross effect integrates the\nsequences of systemic features, driving factors, and the cross effect of these driving factors. While\napplying support vector machine (SVM) regression, it transfers the nonlinear relationship among\nthese sequences to a linear relationship. To test the GM (1, N) model that is based on support vector\nmachine (SVM) with nonlinear effect, the study applies it to forecast the total output of the\npharmaceutical industry. The range of the data is selected from 2005-2017, which the data from\n2005-2013 are used to fit into the model. The GM (1, N) model based on SVM with nonlinear cross\neffect achieves 0.6566 and 0.2956 in its fitted total of relative error and the forecast total of relative\nerror, respectively. The new model presents a more accurate analysis on fitting and forecast\nprecision than the classic GM (1, N) model and GM (1, N) with the linear cross effect model.
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