Parameter optimization of a novel grey model EGM(1, 1, ∑t^c) and its application in China's GDP per capita prediction

The GM(1, 1) model, i.e. the first-order univariate grey model, is the most important grey prediction model, but it is considerable inaccurate in the prediction of fast-growing sequences. To improve model prediction, this paper makes improvements in the following two aspects based on the traditional GM(1, 1) model: (1) this paper improves the accumulated generating sequence of the original sequence, i.e. properly making a quantitative transformation of the traditional accumulated generating sequence; (2) this paper improves the model's structure, i.e. extending the grey action into the superposition power function expression. We call the new extended model the grey EGM(1, 1, ∑t^c) model, i.e. a first-order univariate extended grey model with grey action, which is a superposition power function. The paper gives the EGM(1, 1, ∑t^c) model's parameter estimation method and time response equation for the simulation and prediction. The paper builds a grey EGM(1, 1, ∑t^c) model with the method proposed and compares it to seven other models for predicting China's GDP per capita. Results show that the EGM(1, 1, ∑t^c) model built has high simulation and prediction precision, and its precision is significantly superior to that of the seven comparison models.