非等间距近似非齐次指数序列的灰色建模方法及其优化

传统的GM(1,1)模型在拟合非齐次指数序列时往往存在较大偏差, 针对现实中大量存在的非等间距近似非齐次指数序列, 本文首先根据非等间距灰色模型建模机理, 提出一个非等间距非齐次灰色模型, 推导出模型参数的最小二乘估计及时间响应函数表达式; 其次, 关于模型初始条件, 建立无约束优化模型; 最后, 实证分析表明, 该改进模型在拟合精度和实用性上均有明显改善, 从而拓宽了灰色模型适用范围.

Methods and optimum of grey modeling for approximation non-homogenous and non-equidistant series

There is higher bias on fitting non-homogenous series. For those non-homogenous and non-equidistant series, a non-homogenous and non-equidistant grey model is put forward which is based on the theory of traditional grey model in this paper. In the first, estimates of the parameters and the time respond function are given by least squares. In the second, an unconstrained optimum model is built about initial condition. In the end, empirical analysis shows that the improved model has better performance in fitting and practicality. And so, the application of grey model can be extended.