估计GM(1,1)模型中参数的一族算法

在灰色微分方程中采用了差商代替导数的一系列方法,并结合估计参数的一系列极小化准则,系统地研究了将不同差商或不同差商的线性组合与不同的极小化准则相结合,就可得到估计GM(1,1)模型中参数的一族算法,指出了许多文献给出的算法都属于这一族算法.一般地,由于不同的时间序列满足不同的差商格式或满足不同的差商格式的线性组合,所以应根据不同实际问题的需要,从这一族算法中选择满意的算法.数值结果表明,采用对模型进行精度检验的标准应与估计GM(1,1)模型中参数a、u的极小化准则相一致,这样估计出的参数效果较好.

A Class of Algorithms for Estimating GM(1,1) Model Parameter

Use a group of methods that difference quotient replaces the derivative in grey differential equation, present a great deal minimization criterions of estimating GM(1,1) model parameter, study systematically that different difference quotient or linear combination of different difference quotient combine with different minimization criterion may gain a class of algorithms for estimation GM(1,1) model parameter, point out that the algorithms given in many articles belong to a class of algorithm. Generally, different time series satisfies different difference scheme, or satisfies linear combination of different difference scheme, so, in accordance with the need of different practical problem, the satisfying algorithm is chosen from a class of algorithms. Calculation results show that using model test standard is uniform with minimization criterion of estimation GM(1,1) model parameter, so the result is satisfied.