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目的探讨自回归求和移动平均(autoregressive integrated moving average,ARIMA)季节乘积模型在季节性时间序列资料分析中的应用,建立结核病发病率的预测模型。方法利用重庆市结核病防治所登记的某区1993至2004年结核病新发病例数及该区各年的平均人口数,采用条件最小二乘法估计模型参数,按照残差不相关原则、简洁原则确定模型的结构,依据 Akaike 信息准则(Akaike’s information criterion,AIC)与 Schwartz 的贝叶斯信息准则(Bayesian information criterion,BIC)确定模型的阶数,建立结核病发病率 ARIMA 季节乘积预测模型。结果非季节和季节移动平均参数分别为0.84076和0.46602,t 检验的 P 值均小于0.05,有统计学意义,方差估计值为0.088589,AIC=19.75979,SBC=23.28219,显示模型提取序列中几乎所有的样本相关信息。对模型进行残差白噪声分析,x~2检验统计量的 P 值均大于0.05,表明 ARIMA(0,1,1)(0,1,1)_4NOINT 模型是有效的。结论 ARIMA(0,1,1)(0,1,1)_4NOINT 模型是一种短期内预测精度较高的结核病发病率预测模型。
Objective To explore the application of seasonal multiplication model of autoregressive integrated moving average (ARIMA) in the analysis of seasonal time series data and to establish a predictive model for the incidence of tuberculosis. Methods The number of newly diagnosed cases of tuberculosis and the average number of newborns in each district registered in Chongqing TB Hospital from 1993 to 2004 were estimated by conditional least square method. The model was determined according to the principle of unrelated residuals and conciseness The Akaike’s information criterion (AIC) and Schwartz’s Bayesian information criterion (BIC) were used to determine the order of the models to establish ARIMA Seasonal Product Prediction Model of Tuberculosis Incidence. Results The non-seasonal and seasonal moving average parameters were 0.84076 and 0.46602, respectively. The P values of t-test were all less than 0.05, with statistical significance. The estimated variance was 0.088589, AIC = 19.75979, SBC = 23.28219, showing that almost all Sample related information. The residual white noise of the model was analyzed. The P values of the x ~ 2 test statistic were all greater than 0.05, which indicated that the ARIMA (0,1,1) (0,1,1) _4NOINT model was effective. Conclusion ARIMA (0,1,1) (0,1,1) _4NOINT model is a predictive model of TB morbidity with high short-term prediction accuracy.