A positive real order weakening buffer operator and its applications in grey prediction model

Abstract

Abstract Based on the idea of fractional calculus, reverse accumulated generating operators of real number’s order are proposed in this paper. We claim the set of these operators forms a\xa01-dimensional additive real Lie group, which is isomorphic to\xa0 R . As a direct consequence, the weakening buffer operators of positive real number’s order are constructed. Compared with traditional weakening buffer operators of integer number’s order, this formulation could make finer adjustments on weight distributions between original data sequence by varying the order of weakening buffer operators, which can take a balance between the influence of disturbance components and the tracking speed of parameter estimation. Applications of this construction are used in GM\xa0 ( 1 , 1 ) \xa0model and multiple linear regression models, experimental results show that the proposed buffer operator can effectively improve the prediction accuracy.