重构背景值双变权GM(1,1)中长期预测模型构建

Establishment of Medium and Long Term Prediction Model of Double Variable Weighted GM(1,1) with Reconstructed Background Value

为了解决传统GM(1,1)模型在中长期预测中存在的局限性和较大偏差问题,提高模型预测精度,拓宽其应用范围,结合全信息变权弱化缓冲算子、全信息加权平均法、Newton-Cotes公式和三次牛顿插值公式,从原始数据变换、背景值重构、初始条件优化3个方面对传统GM(1,1)模型进行改进,建立了重构背景值双变权GM(1,1)中长期预测模型。用西安市年供水量统计数据对模型进行精度检验与分析,结果表明精度检验等级为一级,具有很好的预测精度,可用于西安市年供水量的预测。

In order to solve the limitations and large deviations of the traditional GM（1,1） model in medium and long term data predictions,to improve the model prediction accuracy, and to broaden its scope of application, this paper combined with total information variable-weight weakening buffer operator, total information weighted average method, Newton-Cotes formula and cubic Newton interpolation formula, to improve the traditional GM （1,1） model from the three aspects of the original data conversion, background value reconstruction, and initial condition optimization, and established a medium and long term prediction model of double variable weighted GM（1,1） with reconstructed background value. The Xi＇an annual water supply statistics data were used to test and analyze the accuracy of the model. The accuracy test grade reaches to level one, which has good prediction accuracy. It can be used for long term prediction of annual water supply data in Xi’an.