GM(1,1)模型、ARIMA模型及其组合模型在病毒性甲型肝炎发病数中的预测效果比较

目的探讨GM(1,1)模型、单纯自回归滑动平均(autoregressive integrated moving average,ARIMA)模型及其组成的2种组合模型在甲肝发病数预测中的应用。方法利用某省2009年1月-2013年12月的甲肝逐月发病数作为拟合数据,以2014年1-12月的逐月发病数作为预测数据;分别建立GM(1,1)模型、ARIMA模型、GM(1,1)-ARIMA组合模型、变权组合模型,然后根据4个模型的平均绝对百分比误差(mean absolute percentage error,MAPE)、平均误差率(Mean Error Rate,MER)、均方误差(mean square error,MSE)和平均绝对误差(mean absolute error,MAE)评价模型的效果。结果GM(1,1)模型、ARIMA模型、GM(1,1)-ARIMA组合模型和变权组合模型的拟合、预测的MAPE、MER、MSE和MAE依次分别为20.01%,18.35%,115.98,10.96和28.79%,31.84%,32.96,8.01;21.35%,19.52%,120.75,11.66和32.41%,35.65%,36.18,8.97;17.20%,15.69%,88.07,9.07和31.17%,34.17%,34.57,8.60;18.82%,16.99%,107.82,10.15和19.19%,18.67%,20.74,4.70。结论组合模型拟合及预测效果优于单一模型;变权组合模型为最优预测模型。

Comparison of effects of GM(1,1)model,ARIMA model and their combination models in the prediction of monthly reported caseload of viral hepatitis A

Objective To explore the application of grey model GM(1,1),autoregressive integrated moving average(ARIMA)model and two models established on the basis of combination of the above-mentioned models to forecast of caseload of hepatitis A.Methods The data about monthly reported caseload of hepatitis A in a province from January 2009 to December 2013 were used as the fitting data,and the data about monthly reported caseload of hepatitis A from January to December in 2014 as the prediction data.GM(1,1)model,ARIMA model,GM(1,1)-ARIMA combination model and weight changeable combination model were established and the effects of the four models were evaluated based on mean absolute percentage error(MAPE),mean error rate(MER),mean square error(MSE)and mean absolute error(MAE).Results The MAPE,MER,MSE and MAE fitted and predicted by GM(1,1)model,ARIMA model,GM(1,1)-ARIMA combination model and weight changeable combination model were as follows:20.01%,18.35%,115.98,10.96 and 28.79%,31.84%,32.96,8.01;21.35%,19.52%,120.75,11.66 and 32.41%,35.65%,36.18,8.97;17.20%,15.69%,88.07,9.07 and 31.17%,34.17%,34.57,8.60;18.82%,16.99%,107.82,10.15 and 19.19%,18.67%,20.74,4.70.Conclusions The fitting and predictive effects of the combined model are superior to those of the single model.The weight changeable combination model is the optimal prediction model.