| 一类离散灰色预测模型的统一处理方法及应用 |
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| 引用本文： | 罗党,韦保磊.一类离散灰色预测模型的统一处理方法及应用[J].系统工程理论与实践,2019,39(2):451-462. |
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| 作者姓名： | 罗党 韦保磊 |
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| 作者单位： | 华北水利水电大学 数学与统计学院, 郑州 450046 |
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| 基金项目： | 国家自然科学基金（71271086，71503080）；河南省科技攻关计划项目（182102310014）；河南省高等学校重点科研项目（18A630030）；河南省研究生教育优质课程（灰色系统理论） |
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| 摘 要： | 在加权最小二乘框架下构建了离散灰色预测模型DGMP(1,1,N),论证了最小均方误差准则、最小均方相对误差准则和最小平均绝对百分误差准则下的DGM(1,1)模型、NDGM(1,1)模型和NGM(1,1,k~α)模型均是DGMP(1,1,N)模型的特殊形式,给出了模型阶数N取值的判定准则,证明了模型的仿射变换不变性和无偏性.将DGMP(1,1,N)模型运用到人均能源生活消费量预测中,结果表明该模型具有高拟合和预测精度,验证了模型的可行性与有效性.
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| 关 键 词： | 灰色系统 离散预测模型 加权最小二乘法 仿射变换 人均能源生活消费量 |
| 收稿时间： | 2017-06-21 |
A unified treatment approach for a class of discrete grey forecasting models and its application |
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| LUO Dang,WEI Baolei.A unified treatment approach for a class of discrete grey forecasting models and its application[J].Systems Engineering —Theory & Practice,2019,39(2):451-462. |
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| Authors: | LUO Dang WEI Baolei |
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| Institution: | School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China |
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| Abstract: | A weighted least square grey forecasting model termed as DGMP(1,1,N) is proposed, which proves to be the unified form of DGM(1,1) model, NDGM(1,1) model and DGM(1,1,ka) model under least mean square error criterion, least mean square relative error criterion and least mean absolute percentage error criterion. Then, a criterion to determine the value of N in DGMP(1,1,N) model is also put forward. Furthermore, the modeling accuracy proves to be independent on the affine transformation of 1-AGO sequence and it is unbiased for N order homogenous exponential sequence. Finally, DGMP(1,1,N) model is applied to predicting per capita living energy consumption. The result shows that this model is with high fitting and forecasting accuracy, which verified the feasibility and effectiveness. |
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| Keywords: | grey system discrete forecasting models weighted least square method affine transformation per capita living energy consumption |
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