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.

On Novel Nonhomogeneous Multivariable Grey Forecasting Model NHMGM

“…In order to compare the superiority of the proposed model, a numerical example is utilized to validate the simulation accuracy, six different grey forecasting models are built for modeling, and two accuracy criteria are adopted to test the accuracy. The example demonstrates that NHMGM-2 model is superior to NMGM proposed in [20], NMGM model is superior to MGM(1, ) model discussed in [17], and MGM(1, ) model is superior to single variable grey models GM(1, 1) and NGM (1, 1, ). In a word, the novel NHMGM-2 model provides excellent performance compared with traditional classic grey models and presents advantages of dealing with nonhomogeneous multivariable exponential data sequences.…”

“…The novel nonhomogeneous multivariable grey forecasting model NHMGM(1, , , ) is the extension of traditional MGM(1, ) model, and many grey forecasting models can be derived from NHMGM(1, , , ). For example, NMGM(1, , ) studied in [20] can be derived from NHMGM(1, , , ) while =0, and MGM(1, ) model can also be derived from NHMGM(1, , , ) model when =0. In the following, we denote NHMGM(1, , 2 , ) model as NHMGM-2 while =2 in NHMGM(1, , , ) and denote NHMGM(1, , , ) model as NHMGM-1 while =1 in NHMGM (1, , , ).…”

“…In order to compare the forecasting performance of different grey models, we give the time response functions of NMGM(1, , ) [20] and MGM(1, ) [17] for the convenience of the reader. Corollary 9.…”

“…We employ a multiple variable nonhomogeneous data example to demonstrate effectiveness of the novel model in this part. To better reflect the nonhomogeneous superiority of NHMGM(1, , , ) model, this paper chooses NHMGM-2, NHMGM-1, NMGM(1, , ) studied in [20], the traditional grey prediction model MGM(1, ) discussed in [17], the most commonly used GM(1, 1) model, and the single variable nonhomogeneous grey model NGM(1, 1, ) proposed in [15] to compare the simulation and prediction results.…”

“…The most commonly used multivariable grey forecasting MGM(1, ) model is proposed by Zhai et al [17], which can uniformly describe each variable from viewpoint of system analysis, reflected the interactional relation of variables, and performed preferable prediction accuracy for modeling and forecasting in multiple variable system. MGM(1, ) model attracts many researchers attention and has been successfully applied in various fields [18][19][20][21][22]. Dai et al [18] investigated MGM(1, ) model with optimized background value, and evidence of experiment results demonstrated that the optimized MGM(1, ) model had higher forecasting accuracy for monotone sequences and oscillation sequences.…”