ARIMA模型与GM(1,1)模型在痢疾发病数预测中的比较研究

目的 分别应用求和自回归滑动平均模型(autoregressive integrated moving average model, ARIMA)和灰色模型(gray forecast model)GM(1,1)对湖北省痢疾发病数进行预测,比较两种方法的预测效果,为选择更适宜的方法提供依据。方法 分别应用2001－2015年月发病数及年发病数建立ARIMA模型和GM(1,1)模型,用平均误差率(mean error rate,MER)和决定系数(coefficient of determination,R²)评价拟合效果,并采用2016年实际发病数验证预测效果,选择准确性更高的模型对2017－2018年发病数进行预测。结果 建立的ARIMA模型为SARIMA(1,0,0)(0,1,1)₁₂,GM(1,1)模型为(t+1)=-274 126.038e^{-0.067 467t}+293 275.08,两模型的平均误差率(mean error rate,MER)分别为3.55%和14.78%;决定系数(R²)分别为0.993和0.960,2016年实际发病数与两模型预测发病数的残差分别为635和3 240;相对误差分别为16.54%和84.38%,综合考虑各项评价指标采用ARIMA模型对2017－2018年发病数进行预测分别为4 286和4 011。结论 通过拟合及预测评价指标的比较ARIMA模型均优于GM(1,1)模型,可得ARIMA模型对湖北省痢疾发病数的预测比GM(1,1)模型有较明显的优势,能更准确的处理时间序列类型的资料,此预测结果准确具有实用价值,可为卫生防治工作提供依据。

Comparative study of ARIMA model and GM (1,1) modelin predicting the incidence of diarrhea

Objective The autoregressive integrated moving average model (ARIMA) and gray forecast model GM (1,1) were respectively applied to predicting the incidence of dysentery in Hubei Province. The prediction results of the two methods were compared to provide a basis for selecting a more appropriate method. Methods The ARIMA model and GM (1,1) model were established respectively based on the number of monthly cases and the number of annual cases from 2001 to 2015. The fitting effect was evaluated with the mean error rate (MER) and the coefficient of determination (R²), and the prediction effect was verified with the actual number of cases in 2016. The more accurate model was selected to predict the number of cases in 2017-2018. Results The established ARIMA model was SARIMA (1,0,0)(0,1,1)₁₂, the established GM (1,1) model was(t+1)=-274 126.038e^{-0.067 467t}+293 275.08, and the mean error rates (MER) of the two models were 3.55% and 14.78% respectively. The coefficients of determination (R²) were 0.993 and 0.960 respectively, and the residuals of the actual incidence in 2016 and the incidence predicted by the two models were 635 and 3,240 respectively. The relative errors were 16.54% and 84.38% respectively, and the incidence in 2017 and 2018 predicted by the ARIMA model was 4,286 and 4,011 respectively after all evaluation indexes having been taken into consideration.Conclusions According to the model fitness and prediction accuracy, the ARIMA model is superior to the GM (1,1) model. The ARIMA model has obvious advantages over the GM (1,1) model in predicting the number of dysentery cases in Hubei Province, and can process the data of time series more accurately. This prediction results are of practical value, and can provide a basis for health prevention and treatment.