基于动态分析的时滞累积多变量灰色预测模型及其在粮食生产中的应用  

Time-delayed Accumulative Multivariate Grey Prediction Model Based on Dynamic Analysis and its Application in Grain Production

作　　者：罗党 马艳 LUO Dang;MA Yan(School of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《运筹与管理》2024年第12期195-202,共8页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(51979106);华北水利水电大学研究生创新项目(YK2021-113)。

摘　　要：针对经济社会系统中广泛存在的时滞因果问题,通过分析各驱动因素对主系统行为的时滞累积作用以及各驱动因素序列之间存在的非线性关系,构建了基于动态分析的时滞累积多变量灰色ATDGPM(1,N)预测模型,并探讨其参数求解方法。基于动态分析的时滞灰关联向量确定了驱动因素和时滞期;利用粒子群优化算法对幂指数进行优化求解;论证了DGM(1,N),DGPM(1,N)和ATDGM(1,N)模型均是该模型在不同参数取值下的特殊形式。数值实验结果表明ATDGPM(1,N)模型能够更好的描述系统行为序列与驱动因素序列之间的时滞非线性关系,从而有效提高建模精度。将该模型应用于河南省粮食产量的模拟和预测中,可得ATDGPM(1,N)模型的模拟和预测精度远远高于DGPM(1,N)模型和GM(1,N)模型,从而进一步验证了模型的有效性和可行性。As a large agricultural province in China,Henan province holds an important position in the overall situation of national food security,and the forecast of grain production is an important research topic in agricultural economics.This study forecasts the grain production in Henan province and puts forward some suggestions from the perspective of the government’s policy making.Aiming at the widespread time-lag causality problem in economic and social systems,by analyzing the time-lag cumulative effect of each driving factor on the behavior of the main system and the nonlinear relationship between the sequences of each driving factor,we construct a time-lag cumulative multivariate grey ATDGPM(1,N)prediction model based on the dynamics analysis,and explore its parameter solving method.The application scope of the grey multivariate prediction model is broadened from the theoretical method,and some suggestions are provided for the decision-making of government departments from the practical point of view.Based on the data of China Statistical Yearbook and Henan Provincial Statistical Yearbook from 2007 to 2020,this paper constructs a time-lag cumulative multivariate grey ATDGPM(1,N)prediction model based on dynamic analysis,and proposes the“Dynamic Grey Correlation Time-Lag Analysis Method”to determine the time-lag relationship between the sequence of the system behaviors and that of the related factors.By analyzing the time lag relationship between the system behavior sequence and the related factor one,the dynamic grey correlation time lag analysis method is proposed to determine the driving factors and the time lag period;from the perspective of improving the accuracy of the model,with the objective of minimizing the average error of modeling,the known conditions such as the model parameters and the time-response equation are taken as the constraints,the nonlinear optimization model is constructed,and the particle swarm optimization algorithm is utilized for the optimization of the power index.It is argued th

关 键 词：动态分析 时滞累积 ATDGPM(1 N) 粒子群算法 粮食产量预测 

分 类 号：N941.5[自然科学总论—系统科学]