ARMA模型用于预测病毒性甲型肝炎发病趋势

目的探讨应用时间序列ARMA模型对甲肝发病趋势进行预测的可行性,为预防和控制甲肝提供依据。方法采用SPSS 13.0对中山市2004-2009年的甲肝月发病人数资料建立ARMA模型,并对2010年上半年数据进行2步递推预测,通过对拟合残差的白噪声检验评价模型的拟合效果,采用绝对误差百分比、均方根误差评价预测效果。结果 AR（1）是拟合中山市2004-2009年甲肝逐月发病数较为合适的模型,模型为yt=5.137＋0.435yt-1＋at,其AR1系数为0.435（t=4.026,P〈0.001）;模型拟合残差的自相关系数和偏相关系数在不同时刻均无统计学意义,Ljung-Box Q统计量差异无统计学意义（Q=6.609,P=0.636）,残差检验符合白噪声,模型拟合效果良好;绝对误差百分比和均方根误差分别为0.029和0.856,预测效果良好。结论 AR（1）模型能较好的模拟中山市甲肝发病情况,且能较好地预测未来短期内的发病趋势。

Forecasting the incidence trend of the reported viral hepatitis A with autoregressive and moving average model

Objective The study aims to establish an effective prediction model of the monthly reported caseload of viral hepatitis A in Zhongshan City and to provide the basis for prevention and control strategy. Methods Based on the monthly reported caseload of viral hepatitis A in Zhongshan City from January 2004 to 2009,ARMA model was established to forecast the reported caseload of the first half of 2010. The fitness effect was assessed by white noise test of residuals, while predictive ability was evaluated by root mean square error and mean absolute percentage error. Results The best form of ARMA model is yt= 5. 137 ＋ 0. 435yt-1＋ at,in which the autoregression coefficient was 0. 435（ t = 4. 026,P 0. 001）. Both autocorrelation coefficients and partial autocorrelation coefficients of the residuals had no statistical significance in different time,and the Ljung-Box Q-statistic had no statistical significance（ Ljung-Box Q = 6. 609,P = 0. 636） either,which indicate that the residuals follow white noise pattern. The prediction of the reported viral hepatitis A caseload in the first two quarters of 2010 led to good forecasts,with the mean absolute percentage error 0. 029 and root mean square error 0. 856. Conclusions ARMA model is an important tool for fitting the reported caseload of viral hepatitis A,and the short-term trend of incidence can be predicted.