基于优化GM(1,1)模型的安徽省GDP预测

GDP Prediction of Anhui Province Based on Optimized GM(1,1)Model

传统GM(1,1)模型基于最小二乘法进行参数估计,计算过程简单,但易受异常值影响,而最小一乘法考虑误差绝对值和最小,稳健性较好,且背景值z(1)(k)易使GM(1,1)模型产生系统误差。鉴于此,文章提出一种基于优化背景值的最小一乘法GM(1,1)模型。采用传统GM(1,1)模型、背景值优化的GM(1,1)模型和文章中提出的优化背景值的最小一乘法GM(1,1)模型对安徽省2012—2020年的GDP总量进行了建模研究,并对比几种模型的预测精度,发现文章提出的优化GM(1,1)模型预测精度最好。

The traditional GM(1,1)model estimates the parameters based on the least square method,which has a simple computational process but is susceptible to outliers,while the least absolute deviations considers the minimum sum of absolute errors,which is more robust,and the background value z(1)(k)is susceptible to systematic errors in the GM(1,1)model.Therefore this paper proposes a least-squares GM(1,1)model based on optimized background values.The traditional GM(1,1)model,the GM(1,1)model with optimized background values and the least-squares GM(1,1)model with optimized background values proposed in the paper are used to model the total GDP of Anhui Province from 2012 to 2020 and the forecasting accuracy of several models are compared.It has been found that the optimized GM(1,1)model proposed in the paper has the best forecasting accuracy.