Non-equidistant Multivariable Optimizing MGM(1, n) Model Based on Improving Background Value

Abstract Background value is an important factor affecting the precision of non-equidistant multivariable MGM(1, n) model. Based on index characteristic and integral characteristic of grey model GM(1, 1) and improved the method constructing background value, the function with non-homogeneous exponential law was used to fit the one-time accumulated sequence via three points to obtain the background value of non-equidistant multivariable MGM(1, n) model. A new non-equidistant multivariable optimizing MGM(1, n) model based on improving background value was put forward which takes the first component of the original sequence as initial condition, the mean relative error as objective function and the modified values of response function as initial value. The proposed MGM(1, n) model can be used in equidistance & non-equidistance modeling and has the characteristic of higher precision as well as stronger adaptability. Examples validate the practicability and reliability of the proposed model.

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