ARIMA乘积季节模型在上海市甲肝发病预测中的应用

Application of multiple seasonal ARIMA model in forecasting the incidence of hepatitis A in Shanghai

目的应用自回归求和移动平均(autoregressive integrated moving average,ARIMA)乘积季节模型分析季节性时间序列,建立上海市病毒性甲型肝炎发病率的预测模型。方法利用上海市1990年至2011年甲肝按月发病数的历史疫情数据,采用非条件最小二乘法估计模型参数,模型阶数确定后,建立甲肝按月发病数ARIMA乘积季节预测模型。结果非季节和季节移动平均的参数分别是0.6341和0.9999,季节自回归的参数是0.4059,t检验的P值均<0.0001,方差估计值是0.1593,AIC=282.1478,SBC=292.7242,对建立的模型进行残差的白噪声检验,χ2检验统计量的P值均>0.05,据此建立ARIMA(0,1,1)(1,1,1)12NOINT乘积季节模型,模型表达式(1-0.405 9B12)(1-B)(1-B12)Yt=(1-0.634 1B)(1-0.999 9B12)εt,并开展上海市甲肝发病数的预测。结论 ARIMA(0,1,1)(1,1,1)12NOINT乘积季节模型可用于预测上海市病毒性甲型肝炎发病的季节模型。

Objective To explore the application of auto-regressive integrated moving average （ARIMA） model of time series in forecasting the incidence of hepatitis A. Methods ARIMA model was fitted with data of monthly reported cases in Shanghai from Jan. 1990 to Dec. ,2011 for hepatitis A. Parameters were estimated according to unconditional least square method. Multiple seasonal ARIMA model was established for monthly incidence of hepatitis A in Shanghai after index was identified. Results Non-seasonal and seasonal moving average coefficients were 0. 634 1 and 0. 999 9, respectively. Seasonal auto-regressive coefficient was 0.405 9. P values for t-test of all coefficients were all below 0. 000 1. The estimated variance was 0. 159 3, AIC = 282. 147 8, SBC = 292. 724 2. Autocorrelation test for residuals of model was white-noise series. ARIMA （0, 1, 1 ） （1,1,1）12NOINT was identified to fit and forecast monthly hepatitis A cases. Model equation was （1-0.4059B^12）（1-B）（1-B^12）Y,=（1-0.6341B）（1-0.9999B^12）εt. Conclusions The multiple seasonal model of ARIMA can be used to fit trends of incidence for hepatitis A in Shanghai and forecast within short period.