关键词: 灰色预测, GM(1,1)模型, 差分方程, 动态寻优

Abstract: In real life, the prediction accuracy of classical GM(1, 1) model is unstable, and most of the previous optimization methods are one-sided. In this paper, the background and initial values of classical GM(1, 1) model are improved, and a combined optimization method is proposed. According to the principle of dynamic optimization, the background value is set as a variable, and its parameters and time response formula are determined by the minimum value of MRE. At the same time, the difference equation is used to replace the static equation with x⁽¹⁾(1) as the fixed point.Initial and background values are taken as variables to systematically reduce model errors. Combining with the domestic annual oil consumption data, the classical GM(1, 1) model and the improved GM(1, 1) model are used to calculate and compare the errors, which proves that the improved model is significantly better than the classical model in accuracy.

Key words: grey prediction, GM(1,1) model, difference equation, dynamic optimization