上海静安区儿童流感样病例就诊百分比预测的自回归求和移动平均模型构建与应用

Study on the construction and application of ARIMA model to predict the hospital-visiting percentage of children influenza-like illness in Jing'an District,Shanghai

目的探讨构建并应用自回归求和移动平均(autoregressive integrated moving average,ARIMA)模型预测静安区儿童流感样病例(influenza-like illness,ILI)就诊百分比的可行性,为儿童流感流行的早期预警提供科学依据。方法基于2011—2014年上海市静安区的逐月儿童ILI就诊百分比,模型参数确定采用非条件最小二乘法,模型结构依据简洁与残差不相关原则确定,拟合优度以许瓦兹贝叶斯准则与赤池信息准则评估,构建儿童ILI就诊百分比预测的最优ARIMA模型。以模型预测静安区2015年1~10月儿童ILI就诊百分比,计算实际值与预测值的相对误差,并预测静安区2016年的儿童ILI就诊百分比。结果模型ARIMA(1,1,1)(无常数项)对儿童ILI就诊百分比序列拟合良好,自回归参数(AR1=-0.901)与移动平均参数(MA1=0.943)差异均有统计学意义(P<0.001),残差达到白噪声(P>0.05),模型表达式为(1+0.901B)(1-B)Z_t=(1+0.943B)μ_t。2015年1~10月儿童ILI就诊百分比的预测值符合实际值的变动趋势,相对误差最小仅为0.47%。结论 ARIMA模型可以较好地拟合静安区儿童ILI就诊百分比的时间变动趋势,能对ILI就诊百分比进行短期预测,有较好的预测精度。

Objective To explore the feasibility for the construction and application of time series ARIMA model to predict the hospital-visiting percentage of children influenza-like illness（ ILI） in Jing-an District,Shanghai,and provide a basis for early warning of children influenza pandemic. Methods ARIMA model was established based on the monthly visiting percentage of children ILI of Jing-an District from 2011 to 2014. The parameters of the model were estimated through unconditional least squares method,the structure was determined according to the criteria of residual un-correlation and concision. The constructed optimal model was applied to predict the monthly visiting percentage of children ILI in Jing-an District from January to October,2015 and evaluate the validity of the model through comparing the relative error of predicted value with the actual one. The monthly visiting percentage of children ILI in2016 was predicted by ARIMA model based on the data from January 2011 to October 2015. Results The model ARIMA（ 1,1,1）（ no constant） could preferably fit the time series of the visiting percentage of children ILI with both autoregressive coefficient（ AR1 =-0. 901） and moving average coefficient（ MA1 =-0. 943）,being statistically significant（ P 0. 001）. The predicting error was white noise（ P〈0. 05）. The mathematic function was（ 1 ＋ 0. 901B）（ 1-B） Z_t=（ 1 ＋ 0. 943B） μ_t. The predicted value from January to October 2015 was consistent with the actual one,with the minimum relative error of 0. 47%. Conclusion ARIMA model can be used to fit the changes of the hospital-visiting percentage of children ILI in Jing-an District,and forecast the future visiting percentage of children ILI. It is a predicting model of high precision for short-time forecast.