A Novel Dynamic Grey Action Quantity GM(1,1,b) Model and Its Application

The classical GM(1,1) model treats the grey action quantity as an invariant constant, but changes have occurred within the system as time and space change. If the fixed grey action quantity is still used for modeling, the model will have errors. Aiming at this shortcoming, this paper proposes a GM(1,1,b) model in which the grey action quantity can be dynamically changed. Starting from the background value formula, the model solves the grey action quantity at different time points by the development coefficient, and fits the sequence with the DGM(1,1) model, then brings the obtained time response sequence into the classical GM (1, 1) to replaces the grey action quantity constant, so as to establish a GM(1,1,b) model with dynamic change of grey action quantity. Finally, the model is applied to the example of China's rural residents' consumption index. The numerical example shows that the GM(1,1,b) model proposed in this paper effectively improves the prediction accuracy of the model and verifies the effectiveness and practicability of the improved model.