摘要
首先论述了参数d迭代逼近求解的GM(1,1)模型基本思路.其次,给出了此模型的参数估计与算法,即:1)估算出初始a_l,根据GM(1,1)模型a,c,d之间的关系,由a_l求得C_l,d_l;2)迭代d_l→d_(l+1),再计算a_(l+1),c_(l+1)及平均相对误差mape_l,mape_(l+1);3)多次迭代d_l→d_(l+1),直至|mape_(l+1)-mape_l|<ε时,可得mape最小时的最优参数a,c,d值.然后,从理论与实证方面,证明模型是无偏的,且在参数d迭代过程中,a总能取到有意义的值.最后将模型应用于企业技术创新领域之中.
The basic idea of GM(1,1)based on the iterative approximation of parameter d was first discussed.Secondly,the parameter estimation and algorithm of this model were given as follows:1)the initial value,a_l was estimated.Then c_l and di were obtained according to the relationship among a,c and d in GM(1,1)model; 2)iterated d_i to d_(l+i),and then calculated ai+i,ci+i and the average relative error mape_l,mape_(l+1); 3)iterated di to d_(l+1) repeatedly until |mape_(l+1)-mape_l|<ε.And the optimal parameter values of a,c and d could be obtained when the mape was minimal.Thirdly,the model was proved to be unbiased by theoretical and empiric al research.And parameter a obtained a meaningful value in the iterative procedure of parameter d.Finally,this model was applied to the enterprise technology innovation.
引文
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