中文摘要：

鉴于在GM（1，1）预测模型中，灰参数与背景值导致的GM（1，1）模型的残差，本文提出将残差引入到时序中，对时序进行变异，利用不同的曲线回归方程对变异时序进行估计。基于对不同回归方程估计结果的误差分析，选用最佳的回归方程作为GM（1，1）变异时序预测方程；并将预测结果作为GM（1，1）模型的变量k。实例计算表明，变异时序回归GM（1，1）模型具有较高的模拟及预测精度。

英文摘要：

In thepaper, the residual was proposed to introduce to time sequence in view of the residual that was caused by ash parameter and background value in the prediction model of GM （ 1, 1 ） . Time sequence was been taken variation. Different curve regression equations were used to estimate the variation time sequence. It chose the best regression equation as variation time sequence prediction equation of GM （ 1, 1 ） based on the error analysis of the different estimation results. And it used prediction results as variable k of GM （ 1, 1 ） . The example showed that GM （ 1, 1 ） model of time sequence variation regression had high accuracy of simulation and prediction.