ARIMA及Holt-Winters指数平滑模型在河南省肺结核流行趋势预测中的应用

Application of ARIMA and Holt-Winters exponential smoothing models in prediction of pulmonary tuberculosis prevalence in Henan Province

目的:探讨整合移动平均自回归(ARIMA)模型与Holt-Winters指数平滑模型在河南省肺结核流行趋势预测中的应用。方法:收集河南省卫生健康委员会官网上的2013年1月至2022年2月肺结核发病数据,以2013年1月至2020年12月的数据建立时间序列,用以构建ARIMA和Holt-Winters指数平滑预测模型,并用模型预测2021年1月至2022年12月河南省肺结核发病数。结果:河南省肺结核发病具有典型的季节性分布特征,每年3、4月为发病高峰。ARIMA(1,0,1)(2,1,0)_([12])为最终确定的ARIMA模型。Holt-Winters指数平滑模型平滑参数α、β、γ分别为0.218 1,0.000 3和0.000 4,基线level为6 473,slope为-25.82。经Box-Ljung检验,ARIMA模型和Holt-Winters指数平滑模型预测值残差均服从正态分布(χ^(2)=0.219、0.007,P=0.640、0.931)。ARIMA模型预测值的RMSE为374.62,MAPE为5.32%,平均相对误差为10.07%;Holt-Winters指数平滑模型分别为322.65、4.87%和8.12%。结论:两种模型均可用于河南省肺结核流行趋势的预测。

Aim:To investigate the applicability of auto regressive integrated moving average(ARIMA) model and Holt-Winters exponential smoothing model in predicting the epidemic trend of pulmonary tuberculosis in Henan Province.Methods:Reported incidences of pulmonary tuberculosis from January 2013 to February 2022 were collected from the Health Commission of Henan Province.A time series was created with data from January 2013 to December 2020 to construct ARIMA model and Holt-Winters exponential smoothing model,which were utilized to predict the incidence from January 2021 to December 2022.Results:The incidence of pulmonary tuberculosis presented typical seasonal distribution,with high prevalence from March to April every year.ARIMA(1,0,1)(2,1,0)_([12]) was determined as the final model for prediction.The smoothing parameters α,β and γ of Holt Winters exponential smoothing model was 0.218 1,0.000 3 and 0.000 4,respectively,while the baseline level value was 6 473,and the slope value was-25.82.According to Box-Ljung test,the predicted residuals of ARIMA model and Holt-Winters exponential smoothing model followed normal distribution(χ^(2)=0.219,0.007;P=0.640,0.931).The RMSE and MAPE of ARIMA model prediction value were 374.62 and 5.32%,the average relative error was 10.07%.For Holt-Winters exponential smoothing model,they were 322.65,4.87% and 8.12%,respectively.Conclusion:Both models are effective in predicting the incidence of pulmonary tuberculosis in Henan Province.