基于精细积分法的无偏非齐次灰色模型构建

传统无偏灰色预测模型的参数估计和序列模拟都是通过白化方程的离散时间响应函数求取相应的估计值和模拟值.基于精细积分法,提出一种无需求离散时间响应函数的无偏非齐次灰色模型.该模型通过引入新变量,将白化方程转化为齐次矩阵微分方程,利用指数矩阵求得递推关系,进而推导参数无偏估计公式,并采用精细积分法直接计算灰色模型的模拟(预测)值,从而减少舍入误差,提高计算精度.同时,还证明该建模方法具有非齐次指数规律重合性和伸缩变换一致性.严格非齐次指数序列、近似非齐次指数序列、不同类型的单调序列以及汽车保有量预测实例的结果进一步表明,所构建的模型能严格拟合非齐次指数序列,验证了该模型的有效性和实用性,提高了拟合(预测)精度.

An unbiased non-homogeneous grey model based on high precise direct integration method

It is a traditional way to establish parameter estimations and simulations of unbiased grey prediction models by the discrete time response function of whiten differential equation. An novel unbiased grey model based on the high precise direct integration method is proposed without using the discrete time response function. The recurrence relation can be deduced by the exponential matrix of the homogeneous matrix differential equation, written by introducing some new variables, and the unbiased parameters can be derived. Then the simulated values are calculated by using the high precise direct integration method, which can reduce rounding errors and improve precision. It is proved that the proposed method possesses nonhomogeneous law coincidence property and linear transformation consistency. Finally, the validity and utility of the proposed model are verified by rigorous non-homogenous exponential sequence, approximate non-homogenous sequence, monotone sequences and the practical example of car ownership, and the proposed model can improve the precision of simulation and prediction.