An Approach to Improve Estimation Performance of GM(1,1) Model

In this paper, we present an approach to improve estimation performance of GM(1,1) model. It consists of three stages in the GM(1,1) modeling: the preprocessing 1-AGO (first-order accumulated generating operation), first-order difference equation, and 1-IAGO (first-order inverse accumulated generating operation). Note that the solution of first-order difference equation is of exponential form. Therefore, it is assumed that the data after 1-AGO is of exponential-like form. However, in many cases the 1-AGO preprocessed data may not have an exponential-like form. Consequently, an inaccurate modeling results and thus poor performance for GM(1,1) model. Based on the observation, we replace the first-order difference equation in the GM(1,1) modeling with a polynomial to relieve the requirement of exponential-like form in the 1-AGO preprocessed data. By this doing, the estimation performance of GM(1,1) model is improved. Through examples, the proposed approach is justified. As expected, the simulation results indicate that the proposed approach outperforms the conventional GM(1,1) model in the given fitting and forecasting examples.