三参数离散灰色预测模型DGM（1,1）3及其应用

Three-Parameter Discrete Grey Prediction Model DGM（1,1）3 and Its Application

离散灰色预测模型DGM(1,1)解决了传统灰色模型从差分方程到微分方程的跳跃性误差,但是当建模序列存在一定波动时其模拟性能仍不理想文章在传统DGM(1,1)基础上,提出了一种含三参数的离散灰色预测模型DGM(1,1)3,该模型充分考虑了序列滞后项对模拟及预测结果的影响,能在一定程度上改善建模序列光滑性,从而提高模型性能通过对波动序列模拟及预测误差的比较和分析,验证了DGM(1,1)3模型具有比传统的DGM(1,1)及经典GM(1,1)更好的模拟及预测性能、最后将该模型成功地应用于安徽省万人有效发明专利数的模拟及预测研究成果对优化灰色预测模型建模方法,丰富灰色预测模型理论体系具有一定的积极意义。

The discrete grey prediction model DGM (1,1)solves the jumping error of traditional grey model from difference equation to differential equation.However,the simulation performance is still not ideal when the modeling sequence has certain fluctuation.Based on the conventional DGM (1,1),this paper presents a discrete grey prediction model,i.e.DGM(1,1)3 with three parameters.The proposed model takes full account of the influence of lag term on the simulation and prediction results,and can improve the smoothness of a modeling sequence to some degree,thus improving the model performance.And then the paper makes a comparison and analysis of wave sequence simulation and prediction error to verify that the DGM(1,1)3 model has better simulation and prediction performance than traditional DGM(1,1) and classic GM(1,1).Finally,the model is successfully used to simulate and predict the number of effective invention patents per 10-thousand people in Anhui province.The research results have positive significance for optimizing the modeling method of grey prediction model and enriching the theoretical system of grey prediction model.