On Novel Nonhomogeneous Multivariable Grey Forecasting Model NHMGM

Abstract

A novel nonhomogeneous multivariable grey forecasting model termed NHMGM(1,m,kp,c) is proposed in this paper for use in nonhomogeneous multivariable exponential data sequences. The NHMGM(1,m,kp,c) model is able to reflect the nonlinear relation of the data sequences in the system, and it is proved that many classic grey forecasting models can be derived from NHMGM(1,m,kp,c) model. Parameters of the novel model are obtained by using least square method, and the time response function is given. A numerical example is presented to show the effectiveness of the proposed model, six different grey forecasting models are built for modeling, and two popular accuracy criteria (ARPE and MAPE) are adopted to test the reliability of the novel model. The example demonstrates that NHMGM-2 model provides favorable performance compared with the other five grey models. Additionally, the multiplication transformation properties of NHMGM(1,m,kp,c) are systematically analysed, which establish a theoretical foundation for further applications of the model.