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三参数区间灰数序列的矩阵型自回归时滞灰色多变量模型

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已有的灰色预测模型只能间接地预测三参数区间灰数序列，为进一步提高灰色模型对三参数区间灰数的预测精度，在传统灰色模型的基础上考虑时滞效应对系统特征的影响，把系统特征的自回归时滞项引进传统灰色模型，构建了自回归时滞灰色多变量模型。然后进一步把模型变量看作列向量，把参数设置为矩阵的形式，提出了矩阵型自回归时滞灰色多变量模型。该模型保持了三参数区间灰数的完整性，接连了灰数各界点之间的内在关系，能直接对三参数区间灰数序列进行建模和预测。对第二产业总值和第三产业总值的三参数区间灰数序列进行拟合和预测，结果表明，新模型具有比竞争模型更高的精度，具有一定的有效性和实用性。
A Matrix Autoregressive Time-delay Grey Multivariable Model for Three-parameter Interval Grey Number Sequences
The existing grey models can only predict three-parameter interval grey number sequences indirectly,and the influence of time-delay effect is seldom considered.In order to improve the prediction accuracy of grey model for three-parameter interval grey numbers,a new model considering time-delay effect is proposed.Firstly,the autoregressive time-delay terms of system characteristic are introduced into the traditional grey models.Further,a matrix autoregressive time-delay grey multivariable model(MARGM(1,N))is proposed by taking the variables as three-dimensional column vectors and setting the parameters as matrices.The integrity of the three-parameter interval grey numbers is maintained and the relations between the boundaries are connected,so that the three-parameter interval grey number sequences can be modeled and predicted directly by MARGM(1,N).MARGM(1,N)is used to forecast the output of China's secondary industry and tertiary industry.The results show that the models considering the time-delay effect have better fitting effect,the matrix models have higher prediction accuracy,and MARGM(1,N)has the best performance in both fitting and forecasting compared with the competition models.Overall,MARGM(1,N)is feasible and effective.In application,it is helpful for relevant departments to make correct policies to coordinate economic development.

three-parameter interval grey numbersgrey multivariable modelautoregressiontime-delay effect

梅韵杰、曾祥艳、闫书丽

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桂林电子科技大学数学与计算科学学院,广西 桂林 541004

南京信息工程大学管理工程学院,江苏 南京 210044

三参数区间灰数 灰色多变量模型 自回归 时滞效应

国家自然科学基金项目国家自然科学基金项目国家自然科学基金项目国家自然科学基金项目桂林电子科技大学研究生教育创新计划项目桂林电子科技大学研究生思政示范课程建设项目桂林电子科技大学教育教学改革课程建设项目桂林电子科技大学教育教学改革课程建设项目

723610097180106072061007718010852022YCXS138YSZ202309JGKT202348JGKT202351

2024

10.16381/j.cnki.issn1003-207x.2021.0610

中国管理科学
中国优选法统筹法与经济数学研究会 中科院科技政策与管理科学研究所

中国管理科学

CSTPCDCSSCICHSSCD北大核心
影响因子：1.938
ISSN：1003-207X
年,卷(期)：2024.32(9)