上海市原静安区成人流感样病例就诊百分比预测的自回归求和滑动平均模型构建与应用

沈冰; 沈磊; 倪晓芬; 祝军玲; 高洁

doi:10.19428/j.cnki.sjpm.2017.05.004

上海市原静安区成人流感样病例就诊百分比预测的自回归求和滑动平均模型构建与应用

The construction and application of ARIMA model for predicting the hospital-visiting percentage of adult influenza-like illness in Jing-an District of Shanghai

摘要

摘要:
目的探讨构建并应用自回归求和移动平均(autoregressive integrated moving average, ARIMA)模型预测原静安区成人流感样病例(influenza-like illness, ILI)就诊百分比的可行性。
方法基于2011—2014年上海市原静安区的逐月成人ILI就诊百分比，模型参数确定采用非条件最小二乘法，模型结构依据简洁与残差不相关原则确定，拟合优度以许瓦兹贝叶斯准则与赤池信息准则评估，构建成人ILI就诊百分比预测的最优ARIMA模型。以模型预测原静安区2015年1—10月成人ILI就诊百分比，计算实际值与预测值的相对误差；并预测原静安区2016年的成人ILI就诊百分比。
结果模型ARIMA(0, 2, 1)(1, 1, 0)₁₂(无常数项)对成人ILI就诊百分比时间序列拟合良好，移动平均参数(MA1=0.944)与季节自回归参数(SAR1=-0.542)有统计学意义(P＜0.001)，残差达到白噪声(P>0.05)，模型表达式为(1+0.542B)(1-B)² (1-B¹²)Z_t=(1-0.944B)μ_t。2015年1—10月的成人ILI就诊百分比的预测值符合实际值的变动趋势，相对误差最小仅为4.45%。
结论ARIMA模型可以较好地拟合原静安区成人ILI就诊百分比的时间变动趋势，能对成人ILI就诊百分比进行预测，短期预测有较高的精度。

Abstract:
ObjectiveTo explore the feasibility of constructing and applying the autoregressive integrated moving average(ARIMA)model for predicting the hospital-visiting percentage of adult influenza-like illness (ILI) in Jing-an District, Shanghai.
MethodsAn optimal ARIMA model for predicting the hospital-visiting percentage of adult ILI was established based on the monthly hospital-visiting percentage of adult ILI in Jing-an District of Shanghai from 2011 to 2014. The parameters of the model were determined through non-conditional least square method, the structure thereof was determined according to the concision principle and residual non-relevance principle, and the goodness of fit thereof was determined in accordance with Schwarz Bayesian Criterion(BSC) and Akaike Information Criterion (AIC). This model was applied to predict the monthly hospital-visiting percentage of adult ILI in Jing-an District from January to October of 2015 and to calculate the relative error between the actual value and the predicted one; it was also used to predict the monthly hospital-visiting percentage of adult ILI in Jing-an District in 2016.
ResultsThe ARIMA model (0, 2, 1)(1, 1, 0)₁₂ (without constants) could well fit the time series of the hospital-visiting percentage of adult ILI while both the moving average coefficient (MA1=0.944) and the seasonal autoregressive coefficient (SAR1=-0.542) had statistical significance(P < 0.001) and the residual error reached white noise(P>0.05). The mathematic expression of the model was (1+0.542B) (1-B)² (1-B¹²)Z_t=(1-0.944B)μ_t. The predicted value for the hospital-visiting percentage of adult ILI from Jan., 2015 to Oct., 2015 was in conformity with the change trend of the actual value and the minimal relative error was only 4.45%.
ConclusionThe ARIMA model can well fit the time-change trend of the hospital-visiting percentage of adult ILI of Jing-an District and can be used to forecast the hospital-visiting percentage of adult ILI while ensuring relatively high accuracy of short-term forecasts.

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