A nonlinear grey forecasting model with double shape parameters and its application

摘要

The solution of Bernoulli differential equation can be described as a generalized Logistic curve function. Weibull cumulative distribution function is also an analytic solution of one variable coefficient differential equation. But, however because of the exact analytical solution problem of the equation, up to now, the developing coefficient of all the grey forecasting models is still defined as a constant. So, the aim of this paper is just to construct a novel grey differential equation model by combining NGBM(1,1) and Weibull cumulative distribution function. The proposed model(WBGM(1,1)) has the advantages of NGBM(1,1) and Weibull cumulative distribution. Where there are double shape parameters, the developing coefficient of the grey forecasting model is extended to be a variant. Property analysis of WBGM(1,1) shows that the fitting accuracy is higher and the applicable confines are wider. Finally, this paper gives an optimization method for the parameters of WBGM(1,1). A classic example and a practical case are studied for confirming the effectiveness of WBGM(1,1). The case study is the prediction for the number of invention patents of integrated circuit(IC) filed in China from 2007 to 2017. Results of the example and case study are compared to other forecasting models, including GM(1,1), NGBM(1,1), Holt exponential smoothing and ARIMA. Results show that WBGM(1,1) is a more general and more efficient model in grey prediction theory.