Non-equidistant new information optimum GM(1,1) model and its application

Abstract

Grey system is a theory which studies poor information specially, and it possesses wide suitability. Applying the principle in which new information should be used fully and modeling method of grey system, a non-equidistant new information optimum GM(1,1) model is put forward in which the nth component modified by optimization is taken as the initialization and the relation error to least is taken as objective function. As the background value is an important factor affecting the precision of grey system model, based on index characteristic of grey model and the definition of integral, the background value in non-equidistant GM(1,1) model is researched and the discrete function with non-homogeneous exponential law is used to fit the accumulated sequence and optimum formula is given. The formula of background value of new information GM(1,1) model can be used in non-equal interval & equal interval time series. Example validates the practicability and reliability of the proposed model.