Formula Derivation of Parameter n in GM(1,1)Model's Background Value Construction and Its Application

The former could produce a satisfactory result yet the computation is too complicated, while the latter is simple to compute yet is blamed for the lack of a theoretic basis, thus efforts are made to put forth a simple, yet strictly and theoretically based approach to determine the parameter in the background value. The dependence formula of the score n in optimized background value z⁽¹⁾_n(k)and development coefficient a was derived from the strict index sequential form. For the general sequence, the estimation formula of development coefficient is given too. Then based on the dependence formula n is determined, and the optimized background value z⁽¹⁾_n(k)is introduced into gray differential equations to solve the development coefficient a, thus a prediction model with a nice sphere of application and high simulation accuracy is gained. And case-based examples show that the said method is of high feasibility and superiority.