A Nonhomogeneous Multivariable Grey Prediction NMGM Modeling Mechanism and Its Application

Abstract

The purpose of this paper is to explore modeling mechanism of a nonhomogeneous multivariable grey prediction NMGM(1, m, kα) model and its application. Although multi-variable grey prediction MGM(1, m) model has been employed in many fields, its prediction results are not always satisfactory. Traditional MGM(1, m) model is constructed on the hypothesis that original data sequences are in accord with homogeneous index trend; however, the nonhomogeneous index data sequences are the most common data existing in all systems, and how to handle multivariable nonhomogeneous index data sequences is an urgent problem. This paper proposes a novel nonhomogeneous multivariable grey prediction model termed NMGM(1, m, kα) to deal with those data sequences that are not in accord with homogeneous index trend. Based on grey prediction theory, by least square method and solutions of differential equations, the modeling mechanism and time response function of the proposed model are expounded. A case study demonstrates that the novel model provides preferable prediction performance compared with traditional MGM(1, m) model. This work is an extension of the multivariable grey prediction model and enriches the study of grey prediction theory.