基于交互作用的多变量灰色预测模型及其应用

针对传统模型没考虑驱动因素间交互作用关系的缺陷,在充分研究交互作用内涵及传统GM(1,N)模型缺陷的基础上,将线性交互关系的作用项引入GM(1, N)模型的灰作用量,构建基于交互作用的IEGM(1, N)的模型,给出了参数估计公式并提出了两个拓展模型,对拓展模型的适用范围进行研究,证明拓展模型与经典模型是等价的。通过对江苏省高新技术产业产值预测的实际案例,验证新模型的有效性,说明其能够有效解决含有交互作用关系的多因素影响的系统预测问题。

Multivariable grey forecasting model based on interaction effect andits application

To address the drawbacks of traditional GM(1, N ), which do not consider the interaction effects among driving factors, a model, abbreviated as IEGM(1, N ), is proposed by introducing the interactive terms into the GM(1, N ) model after studying the concept of interaction effects and problems of the classic multivariable model. Subsequently, the methods of estimating the parameters are put forward. Then, two derived models are built to extend the application areas of the novel model, and their modeling conditions and application scopes are studied. Finally, an actual example about the output values of high-tech industry in Jiangsu province is studied to demonstrate the efficacy of IEGM(1, N ) and its derived model. Empirical results show that the novel model considering interaction effects can achieve a better simulative and predictive precision than the other two models to solve the forecasting problems of a system, which are affected by many factors having interaction effects.