SARIMA模型在福建省细菌性痢疾风险评估中的应用

Application of SARIMA Model for Risk Assessment of Bacillary Dysentery in Fujian Province

目的采用SARIMA模型对福建省细菌性痢疾发病情况进行预测,为风险评估提供科学的定量数据。方法利用Eviews5.0对福建省1990年1月-2013年12月细菌性痢疾的月发病例数进行SARIMA分析。采用自相关函数和ADF单位根检验判断原序列的平稳性,采取自然对数转化和差分使其平稳,然后利用自相关函数和偏相关函数识别和估计SARIMA模型参数,并对结果进行t检验和Q检验,再利用调整R2、AIC准则和SC准则对模型进行评估。最后进行回代评价和预测分析。结果模型SARIMA(2,1,2)(0,1,1)12、SARIMA(0,1,1)(0,1,1)12和SARIMA(1,1,2)(0,1,1)12参数有统计学意义,残差为白噪声,其中SARIMA(1,1,2)(0,1,1)12为最优模型,表达式为:(1+0.75L)(1-L)(1-L12)log(yt)=(1+0.45L-0.35L2)(1-0.79L12)εt。回代检验平均相对误差为14.72%。2013年预测标准误较小,4-7月预测值与实际值相对误差均低于10%。结论 SARIMA模型可对福建省细菌性痢疾发病情况进行较准确的预测,可为及时、科学地研判传染病风险提供可靠的数据基础。

Objective Forecast the bacillary dysentery incidence of Fujian province through SARIMA model,in order to provide scientific quantitative data for risk assessment. Methods The monthly cases of bacterial dysentery in Fujian province from January,1990 to December,2013 were analyzed for SARIMA using Eviews 5. 0 software. Autocorrelation function and the ADF unit root test were analyzed to determine the stability of the original sequence. Then SARIMA model parameters were estimated through the autocorrelation function and partial correlation function,and the results were evaluated by t-test as well as Q test,after which adjusted R2,AIC and SC criterion were used to estimate those attained models. Finally,results were evaluated through back substitution and forecast. Results The parameters of SARIMA（ 2,1,2）（ 0,1,1）12、SARIMA（ 0,1,1）（ 0,1,1）12and SARIMA（ 1,1,2）（ 0,1,1）12were statistically significant,and the residual was white noise. SARIMA（ 1,1,2）（ 0,1,1）12was the optimal model of those three,and expressed as：（ 1 ＋ 0. 75L）（ 1- L）（ 1- L12） log（ yt） =（ 1 ＋0.45L-0.35L2）（ 1-0. 79L12） εt. The average relative error of back generation forecast tests was 14. 72%,so fitting results were satisfactory. In addition,forecast value of 2013 had a good standard error of mean,in which relative error of April to July were less than 10%. Conclusion SARIMA model could forecast accurately for bacillary dysentery incidence in Fujian province,thus it can provide reliable data base in order to judge the risk of infectious disease more timely and scientifically.