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

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.

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

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.