张家川支气管肺炎月发病率的季节性ARIMA模型

ARIMA Model for the Seasonal Incidence of Bronchopneumonia in Zhangjiachuan

医学卫生领域,疾病受到许多因素的影响,很难用结构式因果模型加以解释,根据其自身变动规律建立时间序列的动态模型则是一种行之有效的方法。据此,本文研究了季节性模型在张家川地区支气管肺炎月发病率中的应用。利用2001年9月至2006年7月张家川地区支气管肺炎月发病率资料绘制出时序分布图,观察到该疾病高发在每年12月左右,且有季节性趋势;作偏相关和自相关图,根据模型定阶原则,且残差没有自相关性,进行时间序列模型拟合;最终得到时间序列模型ARIMA(1,0,1)×(2,1,1)12,及其相关数学表达式(1-0.517B)(1+0.784B12+0.137φ2B24)(1-B)12Δ11Zt=(1+0.196B)(1+0.876B12)at,并进行实际值与预测值的比较,估计值虽然与实际值有差异,但基本趋势一致。因此,应该充分考虑各时间段的发病特征,以便更有重点地进行健康防治,有效降低支气管肺炎对人类的危害,保障人类的生活品质。

A disease is usually affected by many factors, so it is difficult to use a structure-based model to explain its cause and effect. A dynamic model of time series established according to its own variations is an effective method to study the seasonal incidence of bronchopneumonia in Zhangjiachuan. This model is applied to the data from September 2001 to July 2006 in Zhangjiachuan region for temporal distribution of bronchopneumonia incidence, A high incidence of the disease each year in December is identified. Seasonal trends, partial correlations and autocorrelations are analyzed in accordance with the principles of model order determination, and no autocorrelation of residuals is found. The final time series model is obtained with related mathematicalexpressions, and the comparison indicates that the estimated results agree with the basic trend.