The improved grey model by fusing exponential buffer operator and its application

To address the issues of insufficient utilization of data and fixed structure of grey model [GM (1,1)], this paper develops an exponential buffer operator based on the new information and variable parameter principles. Measuring and modifying the fluctuation trend of original data is an obvious advantage of this new buffer operator. Further, we prove the weakening, smoothness, new-information, and incremental-innovation properties of the exponential buffer operator. Then, the improved GM (1,1) model is proposed by combining the GM (1,1) model with the exponential buffer operator. This new model combines the fitting advantages of the GM (1,1) model in small sample environment and the additional advantages of the buffer operator of dealing with disturbance factors. Also, we compare the proposed buffer operators with the general buffer operator and the improved GM (1,1) model with the GM (1,1) model. It is found that not only the improved GM (1,1) model can effectively weaken the fluctuation trend in original data sequence, it also reduces forecasting errors and improves the calculation accuracy under the fluctuation small-sample environment. Finally, based on an empirical forecasting of the coal consumption in China, we demonstrate the feasibility and effectiveness of the improved GM (1,1) model and exponential buffer operator.