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.
Highlights
Grey system theory has been adopted to various aspects of fields including energy, environment, industry, and so on [1,2,3]
Ma et al [16] utilized the kernel method to build a novel kernel regularized nonhomogeneous grey model abbreviated as KRNGM, and the results showed that KRNGM model outperformed the existing grey prediction models
This study proposes a novel nonhomogeneous multivariable grey forecasting model NHMGM(1, m, kp, c) and discusses its properties
Summary
Grey system theory has been adopted to various aspects of fields including energy, environment, industry, and so on [1,2,3]. This study proposes a novel nonhomogeneous multivariable grey forecasting model NHMGM(1, m, kp, c) and discusses its properties. The whitenization differential equations of the novel nonhomogeneous multivariable grey forecasting model abbreviated NHMGM(1, m, kp, c) are defined as follows: dx(11) (t) dt. Assume that Γ, α, and βare the parameters of NHMGM(1, m, kp, c) model constructed by the original data matrix X(1) = (X(11), X(21), . If Γ, α, and βare the parameters of transformed NHMGM(1, m, kp, c) model constructed by the multiplication transformation data matrix Y(1) = (Y1(1), Y2(1), . It is not suitable to predict by applying different multiplication transformations to original data when constructing a NHMGM(1, m, kp, c) model
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