On the improvement of the parameter estimation of the grey model GM(1,1) and model application

Abstract The GM(1,1) model has been applied widely for grey prediction. However, traditional GM(1,1) model prediction sometimes results in large errors. In recent years, the grey model GM(1,1) has been improved, and the research mainly focuses on the modification, extension, and optimization of it. Most of the methods change the basic structure of the model. The study aims to improve the model’s parameter estimation without changing the model’s structure by using the following four methods: (1) optimizing the generating coefficient and estimating the model’s parameters in the case of the optimal generating coefficient; (2) using the approximation by polynomial to estimate the model’s parameters as a whole, including the parameter estimation of initial value; (3) translating the grey differential equation into the difference equation to estimate the model’s parameters with the difference equation; and (4) using the modern intelligent algorithm (that is, the improved particle swarm optimization algorithm) for parameter estimation. The study builds the GM(1,1) model of the total consumption of China’s industrial crude oil using the four improved methods. The simulation and prediction results show that these methods all significantly improve the prediction accuracy of model.