Improved methods for parameter estimation of gray model GM(1,1) based on new background value optimization and model application

Abstract

In the gray prediction, the GM(1,1) model has been applied widely, but the conventional GM(1,1) model prediction shows big errors sometimes. Many researchers improve prediction accuracy by changing the basic structure of model. The paper tries to make improvements in the models parameter estimation on the basis of new background value optimization without changing the models structure, and gives the following four methods: (1) estimating the parameter of gray model GM(1,1) with the optimized value of exponential curve as the background value; (2) estimating the parameter of gray model GM(1,1) with the optimized value of power function curve as the background value; (3) estimating the parameter of gray model GM(1,1) with the optimized value of polynomial curve as the background value; (4) estimating the parameter of gray model GM(1,1) with the optimized value of interpolation function as the background value. The last part of the paper builds the GM(1,1) model of China’s total clean energy consumption with the four improved methods. The simulation and prediction results show that these methods all improve the prediction accuracy of model significantly.

Keywords:

• Gray prediction
• Parameter estimation
• Background value
• Simulation and prediction

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F99
• 93A30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors are grateful for the National Natural Science Foundation of China (11401418).