The development of GM(1,1) error toolbox

In the prediction research, the main purpose is to minimize the prediction error; however, the goals cannot be fulfilled completely. Even we choose GM(1,1) model, we also need to minimize the prediction error. Hence, in this paper, we first focus on the influence parameter α in GM(1,1) model, then, analyze the characteristics of α step by step. Second, we give up the α = 0.5 method, and use numerical method to find the prediction error corresponding with α value and plot the figure of the function of error. Finally, after the mathematics model has been presented; we also develop a toolbox, which based on C language to assist us to implement our approach. Consequently, we conclude that the value of α is adaptive in the interval of [0,1] in GM(1,1) model.