近似非齐次指数序列的离散GM(1,1)模型的建立及其优化

Creation of Non-homogenous Discrete GM(1,1) Model and Its Optimization

分析了GM(1,1)模型的缺陷,指出其白化响应式并不是灰微分方程的真正解。建立了近似非齐次指数序列的离散GM(1,1)模型,证明了其可以完全拟合非齐次指数序列。建立了加权背景值下的近似非齐次指数序列的离散GM(1,1)模型,实例证明不同的权值下,其预测精度是不一样的,同时由于该模型默认经过初始值点,这与最小二乘法的思想不符,因此在优化权值的同时优化初始值。实例验证结果表明优化的近似非齐次指数序列的离散GM(1,1)模型提高了预测精度。

The defect of GM （ 1, 1 ） model is analyzed. It is found that the whitenization responsive formula is not the real solution of grey differential equation, and discrete GM （ 1, 1 ） model is built. Although it can avoid the defect of GM （ 1, 1 ） model, the simulative sequence of discrete GM （ 1, 1 ） model is still an exponential sequence. To expand the applied range of discrete GM （ 1, 1 ） model, a non-homogenous discrete GM （ 1, 1 ） model is created, and it is completely fitting a non-homogenous exponential sequence. Based on the modeling mechanism of RGM （ 1, 1 ） model, the weighted non-homogenous discrete GM （ 1, 1 ） model is developed. When the original data is close to a non-homogenous exponential sequence, the forecasting precision varies with the value of weights, so pattern search method is put forward to work out the best weights. Because the weighted model pretermits the initial point and this is not the purpose of least squares technique, so the initial value is also optimized together with weights. Test results show that the optimized weighted non-homogenous discrete GM （ 1, 1 ） rondel can improve forecasting precision.