Grey Modeling Method And Its Application On Prediction

Grey system theory is one of the main methods to study and solve some uncertain problems in the real world. The grey prediction model is an important part of grey system theory as well as a belt to connect the grey system theory and practical application. It has important theoretical significance and practical significance to deeply study the grey prediction model. Because the study on the grey prediction model would not only promote the development of grey system theory but also expand the application scope of grey system theory. The grey prediction modeling technology has achieved better findings after the development for more than 30 years. However, as an emerging discipline, the theory system of grey prediction model still need be further enriched and perfected. This paper studies the interval grey number prediction model, grey prediction model of dual heterogeneous sequence of interval grey number and discrete grey number as well as the optimization model of NGM(1,1,k) model of approximate non-homogeneous exponential increasing sequence based on the summary of classical GM(1,1) model, grey prediction model of grey number sequence and grey prediction model of approximate non-homogeneous exponential sequence. However, the modeling of both GM(1,1) model and its extended model are based on the accumulative generation, and they are suitable for the simulation and prediction of exponential increasing sequence, but there existes great errors for the exponential decreasing sequence. Hence, this paper also studies the reverse accumulative GOM(1,1) model to offset the deficiency of simulation and prediction for approximate non-homogeneous decreasing sequence. Finally, the grey combination prediction model based on grey correlation degree is used to predictively study the financing development of enterprise bond in China. The main contents of this paper are as follows.(1) Study on construction of interval grey number prediction model. From two definitions of "information domain" and "core" of interval grey number, the information domain sequence and cognitive degree sequence of interval grey number are calculated, and the DGM(1,1) model of the two sequences is constructed, respectively. In combination of the two models, the prediction models of upper bound sequence and lower bound sequence of interval grey number are derived. Moreover, under the premise of no loss of existing information, the algebraic operation among grey numbers is avoided, the simulation and prediction of interval grey number are realized, and then the modeling objects of grey prediction model are expanded from real sequences to grey number sequences. This enriches and perfectes the theory system of grey prediction model.(2) Study on the grey prediction model of discrete grey number and interval grey number. The secondary interval grey number which has the same number of grey elements as discrete grey number is obtained by the even partition for interval grey number, thus realizing the “homogenization” conversion of grey heterogeneous data. Then the grey prediction model of dual heterogeneous data sequence related to interval grey number and the discrete grey number is constructed, as well as the modeling mechanism, modeling steps and modeling process of this model are discussed in detail. Finally, the grey modeling object of grey prediction model are expanded from “homogeneous sequence” to the grey “heterogeneous sequence”, as well as the application scope of grey prediction model is expanded.(3) Study on NGM(1,1,k) model optimization of approximate non-homogeneous exponential increasing sequence. On the one hand, from the time response function of NGM(1,1,k) model, the function recursion relationship among the accumulative sequences is derived, and the direct estimation method to solve the parameter values of time response function is presented. Simultaneously, a kind of new NGM(1,1,k) model which can simulate both the approximate homogeneous and approximate non-homogeneous exponential sequences at the same time is constructed, and this model avoides jumpy error of model parameter estimation from difference equation to differential equation. Moreover, the reasons that the new model could simulate the homogeneous exponential sequence and non-homogeneous exponential sequence are theoretically explained, and the initial values of the new NGM(1,1,k) model are optimized. On the other hand, it is concluded that the existing background value construction method of NGM(1,1,k) model is the main reason to cause the model parameter estimation errors by analysis. The NGM(1,1,k) model with optimized background values is derived, the modeling steps of NGM(1,1,k) model with optimized background values is obtained, and finally, the effectiveness of NGM(1,1,k) model with optimized background values is comparatively analyzed by algorithm cases.(4) Expanding study on GOM(1,1) model of homogeneous exponential decreasing sequence. The inhomogeneous expansion study is conducted on GOM(1,1) model based on the GOM(1,1) model, as well as the NGOM(1,1,k) model suitable for approximate non-homogeneous decreasing sequence is constructed. Then the background value of NGOM(1,1,k) model is further optimized to build the NGOM(1,1,k) model with optimized background value. Furthermore, the model property is studied, and its modeling method and steps are presented. Finally, the NGOM(1,1,k)model is expanded from “the homogeneous exponential decreasing sequence” to “the non-homogeneous exponential decreasing sequence”.(5) Predictive study on enterprise bond financing development in China by use of grey correlation combination prediction model. Enterprise bond is an important part of capital market, but enterprise bond financing development in China is affected by many factors. Hence, from the perspective of grey modeling method, grey correlation analysis is conducted on many factors affecting the enterprise bond financing development in this paper, and the main factors affecting the enterprise bond financing development are finally found out. Thus, the grey correlation combination prediction model based on grey correlation degree is constructed to predict the enterprise bond financing development in China, which would provide theoretical basis for development planning of enterprise bond market.