Research on Extension of GM(1,1) and Its Modeling Mechanism

As a basic prediction model, GM(1,1) is widely used. Although the grey forecasting model has been successfully adopted in various fields and demonstrated promising results, the literatures show its performance could be further improved. For this purpose, the paper proves that the growth rate of the simulated value of the grey GM(1,1) is a fixed value. If the growth rates of the primary sequence are equate, the fitted value deriving from GM(1,1) is the same as the primary sequence, otherwise greater error would occur. In order to overcome shortcoming of the fixed growth rates, GM(1,1) is extended by introducing linear time-varying terms. A novel forecasting model is proposed, termed EGM(1,1). Meanwhile, by contrasting EGM(1,1) model to the GM(1,1) model, the result shows that EGM(1,1) model has largely improves fitting and predicting precision.