一次函数变换GM(1,1)模型分析及直接离散GM(1,1)模型的建立

Analysis of GM(1,1) Model Based on Linear Function Transformation and Establishment of Direct Discrete GM(1,1) Model

分析了基于一次函数变换的GM(1,1)模型提高预测精度的实质,即模拟序列从原有的纯指数序列变成了非齐次指数序列,并指出提高光滑度并不是提高预测精度的决定性条件,建立了模拟序列为非齐次指数序列的直接离散GM(1,1)模型.该模型不对原始数据做任何改变,实例应用结果表明其预测精度同一次函数变换的GM(1,1)模型相当,指出了改变模拟序列特征使其更接近于原始数据的发展,对于提高预测精度更具意义.

To analyze the substance of improving forecasting precision of GM（1,1） based on linear function transformation,which is that the simulative sequence is changed from an exponential sequence to a non-homogenous exponential sequence,the fact that the improvement of smoothness is not the prerequisite to improve forecasting precision.The direct discrete GM（1,1） model is built whose simulative sequence is a non-homogenous exponential sequence.The original data of direct discrete GM（1,1） model are not changed before modeling. Test results show the forecasting precision of direct discrete GM （1, 1 ） model is equivalent to that of linear function transformation GM（ 1,1 ） model, so the method to change the characteristic of the simulative sequence to make it be more close to the development of original data is more significative.