组合模型与单一模型在HFRS拟合及预测中的效果比较

Comparison of the effects of combined model and single model in HFRS incidence fitting and prediction

目的比较组合模型与单一模型在(hemorrhagic fever with renal syndrome,HFRS)拟合及预测中的预测效果,为优化HFRS预测模型提供参考。方法以近年来全国发病率最高的黑龙江省作为研究现场,收集2004—2017年黑龙江省HFRS逐月发病率数据。2004—2016年黑龙江省HFRS逐月发病率作为训练数据,2017年1~12月数据作为测试数据。训练数据分别训练SARIMA、ETS和NNAR模型。利用方差倒数法、粒子群优化算法(particle swarm optimization,PSO)分别计算SARIMA、ETS和NNAR模型系数,构建组合模型A、组合模型B。利用建立模型预测2017年1~12月HFRS发病率。5个模型拟合值与训练数据、预测值与测试数据比较,采用平均绝对误差百分比(mean absolute percentage error,MAPE),平均绝对误差(mean absolute error,MAE),均数标准差(root mean squared error,RMSE)和平均误差率(mean error rate,MER)评价模型拟合及预测效果。结果SARIMA最优模型为SARIMA(1,0,2)(2,1,1)12。ETS最优模型为(M,N,M),平滑参数α=0.738,γ=1*10^(-4)。NNAR最优模型为NNAR(13,1,7)12。3个单一模型残差均为白噪声(P>0.05)。组合模型A表达式为y=0.134×y_(SARIMA)+0.162×y_(ETS)+0.704×y_(NNAR);组合模型B表达式为y=0.246×y_(SARIMA)+0.435×y_(ETS)+0.319×y_(NNAR)。SARIMA、ETS、NNAR、组合模型A、组合模型B拟合的MAPE、MAE、RMSE、MER分别为24.10%、0.11、0.17、23.29%;17.14%、0.08、0.14、17.96%;6.33%、0.02、0.03、4.25%;9.03%、0.03、0.05、7.51%;13.16%、0.06、0.09、12.33%。SARIMA、ETS、NNAR、组合模型A、组合模型B预测的MAPE、MAE、RMSE、MER分别为18.70%、0.05、0.06、19.62%;23.83%、0.06、0.07、24.49%;28.30%、0.07、0.10、29.21%;21.69%、0.06、0.08、22.63%;17.39%、0.05、0.07、18.76%。结论组合模型拟合及预测效果优于单一模型。基于PSO计算单一模型权重的组合模型为最优模型。

Objective To compare the prediction effect of combined model and single model in HFRS incidence fitting and prediction,and to provide a reference for optimizing HFRS prediction model.Methods The province with the highest incidence in China(Heilongjiang Province)in recent years was selected as the research site.The monthly incidence data of HFRS in Heilongjiang Province from 2004 to 2017 were collected.The data from 2004 to 2016 was used as training data,and the data from January to December 2017 was used as test data.The training data was used to train SARIMA,ETS and NNAR models,respectively.The reciprocal variance method and particle swarm optimization algorithm(PSO)were used to calculate the model coefficients of SARIMA,ETS and NNAR,respectively,to construct combined model A and combined model B.The established models were used to predict the incidence of HFRS from January to December 2017.The fitted and predicted values of the five models were compared with the training data and test data,respectively.Mean absolute percentage error(MAPE),mean absolute error(MAE),root mean standard deviation(RMSE),and mean error rate(MER)were used to evaluate the model fitting and prediction effects.Results The optimal SARIMA model was SARIMA(1,0,2)(2,1,1)12.The optimal ETS model was ETS(M,N,M),and the smoothing parameterα=0.738,γ=1*10^(-4).The optimal NNAR model was NNAR(13,1,7)12.The residuals of the three single models were white noise(P>0.05).The expression of combined model A was y=0.134×y_(SARIMA)+0.162×y_(ETS)+0.704×y_(NNAR);the expression of combined model B was y=0.246×y_(SARIMA)+0.435×y_(ETS)+0.319×y_(NNAR).The MAPE,MAE,RMSE,and MER fitted by SARIMA,ETS,NNAR,combined model A and combined model B were 24.10%,0.11,0.17,23.29%;17.14%,0.08,0.14,17.96%;6.33%,0.02,0.03,4.25%;9.03%,0.03,0.05,7.51%;13.16%,0.06,0.09,12.33%,respectively.The MAPE,MAE,RMSE,and MER predicted by the five models were 18.70%,0.05,0.06,19.62%;23.83%,0.06,0.07,24.49%;28.30%,0.07,0.10,29.21%;21.69%,0.06,0.08,22.63%;17.39%,0.05,0.07,18.76%,respectively.Conclusion The fitting and prediction effects of the combined models are better than the single models.The combined model based on PSO to calculate the weight of the single model is the optimal model.