季节分解法和ARIMA法预测乌鲁木齐市肺结核发病趋势效果分析

Seasonal decomposition and ARIMA methods in prediction of tuberculosis incidence in Urumqi,China

目的比较时间序列季节分解法和差分自回归滑动平均(ARIMA)法预测肺结核发病趋势的效果,为肺结核预测预警提供科学依据。方法对新疆乌鲁木齐市2005年1月至2014年12月肺结核月发病率时间序列分别构建季节分解拟合模型和ARIMA拟合模型,对2015年各月发病率分别进行预测并与实际发病率进行比较。结果乌鲁木齐市肺结核流行表现出春季高发的年度周期性。应用季节分解法构建的拟合模型中,线性模型和三次曲线模型对2015年各月发病率预测结果的平均绝对百分误差(MAPE)分别为18.75%和92.25%,线性模型预测值整体上低于实际值,三次曲线模型预测值整体上高于实际值;应用ARIMA方法构建的拟合模型为ARIMA(2,1,1)(1,1,0)_(12),对2015年各月发病率预测结果的MAPE为9.46%,整体上预测值和实际值无明显差异。结论ARIMA法较季节分解法对乌鲁木齐市肺结核发病率的预测效果更佳。

Objective To compare the accuracy of the seasonal time series decomposition method and autoregressive integrated moving average（ARIMA） in the prediction of incidence of tuberculosis（TB） in order to facilitate early-warning.Methods The seasonal decomposition model and ARIMA model were constructed by SPSS20.0 software based on time series of monthly TB incidence between January 2005 and December 2014 in Urumqi,China.The obtained models were used to forecast the monthly incidence in 2015 and compared with the actual incidence respectively.Results Between2005 and 2014,the incidence of TB was higher during March,April and May in Urumqi.A linear fitting model and a cubic curve fitting model were constructed by the time series seasonal decomposition method.The mean absolute percentage error（MAPE） of each predicted monthly incidence in 2015 was 18.75% and 92.25%,respectively.The predicted values of the linear model were lower than actual values and the predicted values of the cubic curve model were higher than actual values.An ARIMA（2,1,1）（1,1,0）12fitting model was established by ARIMA method.The MAPE of each predicted monthly incidence in 2015 was 9.46% and there were no significant differences between the predicted and actual values.Conclusion The ARIMA method is better than the seasonal decomposition method for predicting the monthly incidence of TB in Urumqi.