几种改进的灰色模型在广西年用水量预测中的比较研究

Comparative Study of Several Improved Grey Models in Forecasting Annual Water Con-sumption in Guangxi

摘要: 文中基于广西壮族自治区2011~2020年的年用水量数据，采用传统GM(1,1)模型预测，存在精度不足的问题。为了提高预测的准确性，对传统GM(1,1)模型采用四种改进方法，分别是原始序列数据通过函数变换、对GM(1,1)模型预测后的残差修正、对初始序列的弱化算子处理后建模以及本文作者提出的对数变换后灰色建模。通过对比预测结果精度和操作难易程度，发现预测精度四种方法分别为99.32%，99.61%，99.87%，99.75%；从操作难易程度上看，弱化算子法需要对原始数据进行一阶、二阶弱化处理后，再进行一次累加生产法构建模型，整个流程相对复杂，函数变换法和修正误差法操作难度也高于对数变换法，但低于弱化算子处理法，对比之下，对数变换后灰色建模法便有了价值，对于精度要求不是最高的，同时又希望快速估算结果的时候就很有价值。

Abstract: In the paper, based on the annual water consumption data of Guangxi Zhuang Autonomous Region from 2011 to 2020, the traditional GM(1,1) model was used for prediction, which had the problem of insufficient accuracy. In order to improve the accuracy of prediction, four improvement methods are used for the traditional GM(1,1) model, which are the original sequence data through function transformation, residual correction after prediction of the GM(1,1) model, modeling after processing of the weakening operator of the initial sequence, and gray modeling after logarithmic transfor-mation proposed by the authors of this paper. By comparing the accuracy of prediction results and the ease of operation, it is found that the four methods of prediction accuracy are 99.32%, 99.61%, 99.87%, and 99.75%, respectively; in terms of the ease of operation, the weakening operator method requires first-order and second-order weakening processing of the original data and then a cumulative production method to construct the model, and the whole process is relatively compli-cated, and the operational difficulty of the function transformation method and the correction error method is also higher than the logarithmic transformation method, but lower than the weakening operator processing method. In contrast, the gray modeling method after logarithmic transfor-mation is valuable, and it is valuable for those whose accuracy requirements are not the highest, and who also want to estimate the results quickly.