上海市痢疾发病率预测自回归求和移动平均模型的构建与应用

Establishing and applying of autoregressive integrated moving average model to predict the incidence rate of dysentery in Shanghai

目的探讨构建并应用自回归求和移动平均（autoregressive integrated moving average，ARIMA）模型预测上海市痢疾发病率的可行性。方法基于1990--2007年上海的逐月痢疾发病率，采用非条件最小二乘法估计模型参数，按照残差不相关原则与简洁原则确定模型结构，依据赤池信息准则（Akaike information criterion，AIC）及许瓦兹贝叶斯准则（Schwarz Bayesianc riterion，SBC）确定模型的拟合优度，建立预测上海痢疾发病率的最优ARIMA模型。用所得模型预测上海2008年的痢疾发病率，比较预测值与实际值的差异；再以1990年1月至2009年6月的数据构建模型预测上海2010年的痢疾发病率。结果模型ARIMA（1，1，1）（0，1，2）。：较好拟合了既往时间段痢疾发病率的时间序列，模型自回归参数（ARI=0．443）、移动平均参数（MA1=0．806）与季节移动平均参数（SMA1=0．543、SMA2=0．321）均有统计学意义（P〈0．01），AIC值=2．878，SBC值=16．131，模型残差为白噪声，模型数学函数式为（1—0．443B）（1-B）（1-B^12）Zt=（1—0．806B）（1—0．543B^12）（1—0．321B^2×12）μ。2008年逐月痢疾发病率的预测值符合实际值的变动趋势，全年发病率预测值与实际值的相对误差率为6．78％。预测2010年上海市痢疾发病率为9．390／10万。结论ARIMA模型可以较好地拟合上海市痢疾发病率的时间变化趋势，并可用于预测未来的痢疾发病率，是一种短期预测精度较高的预测模型。

Objective To explore the feasibility of establishing and applying of autoregressive integrated moving average （ARIMA） model to predict the incidence rate of dysentery in Shanghai, so as to provide the theoretical basis for prevention and control of dysentery. Methods ARIMA model was estabhshed based on the monthly incidence rate of dysentery of Shanghai from 1990 to 2007. The parameters of model were estimated through unconditional least squares method, the structure was determined according to criteria of residual un-correlation and concision, and the model goodness-of-fit was determined through Akaike information criterion （ AIC ） and Schwarz Bayesian criterion （ SBC ）. The constructed optimal model was applied to predict the incidence rate of dysentery of Shanghai in 2008 and evaluate the validity of model through comparing the difference of predicted incidence rate and actual one. The incidence rate of dysentery in 2010 was predicted by ARIMA model based on the incidence rate from January 1990 to June 2009. Results The model ARIMA （ 1,1,1 ） （0,1,2）12 had a good fitness to the incidence rate with both autoregressive coefficient （ARI = 0. 443 ） during the past time series, moving average coefficient （MA1 = 0. 806） and seasonal moving average coefficient （SMA1 = 0.543, SMA2 = 0.321 ） being statistically significant（P 〈 0. 01 ）. AIC and SBC were 2. 878 and 16. 131 respectively and predicting error was white noise. The mathematic function was （ 1 - 0. 443B） （ 1 - B） （ 1 - B^12） Z, = （ 1 - 0. 806B） （ 1 - 0. 543B^12 ） （1-0. 321B^2×12）μt. The predicted incidence rate in 2008 was consistent with the actual one, with the relative error of 6.78%. The predicted incidence rate of dysentery in 2010 based on the incidence rate from January 1990 to June 2009 would be 9. 390 per 100 thousand. Conclusion ARIMA model can be used to fit the changes of incidence rate of dysentery and to forecast the future incidence rate in Shanghai. It is a predicted model of high precision for short-time forecast.