SARIMA模型参数设置探讨

目的 比较不同参数设置的SARIMA模型拟合及预测效果,为提高SARIMA模型精度提供参考。 方法 利用全国2009年1月—2015年6月手足口病逐月发病率数据,按照传统图示法确定参数p,q值,建立SARIMA模型,记为模型1。再将参数p,q值±1,构建多个备选模型,筛选最优模型,记为模型2。利用模型1和模型2预测2015年7—10月手足口病发病率并与实际值比较,采用平均绝对误差百分比(mean absolute percentage error,MAPE)、平均误差率(mean error rate,MER)、均方误差(mean square error,MSE)和平均绝对误差(mean absolute error,MAE)评价模型拟合及预测效果。 结果 模型1为SARIMA(1,0,0)(1,1,0)₁₂;模型2有2个,包括SARIMA(1,0,1)(1,1,0)₁₂和SARIMA(1,0,1)(0,1,1)₁₂。SARIMA(1,0,0)(1,1,0)₁₂、SARIMA(1,0,1)(1,1,0)₁₂和SARIMA(1,0,1)(0,1,1)₁₂拟合的MAPE依次分别为22.891%、20.015%、19.985%。SARIMA(1,0,0)(1,1,0)₁₂、SARIMA(1,0,1)(1,1,0)₁₂和SARIMA(1,0,1)(0,1,1)₁₂预测的MAPE、MER、MSE和MAE依次分别为9.119%、8.988%、1.874%和1.107%;11.000%、10.909%、2.552%和1.344%;8.711%、8.477%、1.857%和1.044%。 结论 SARIMA(1,0,1)(0,1,1)₁₂为最优模型,拟合及预测效果优于图示法建立的SARIMA(1,0,0)(1,1,0)₁₂模型。在SARIMA建模过程中应在图示法基础上采用凑试法,筛选最优参数,提高模型精度。

Discussion on parameter setting of SARIMA model

Objective To compare the fitting and prediction effects of SARIMA models with different parameter settings, and to provide a basis for improving the accuracy of SARIMA model. Methods The monthly incidence rates of hand, foot and mouth disease (HFMD) in China from January 2009 to June 2015 were collected. The parameters p and q were determined according to the conventional graphic method, and the SARIMA model was established and recorded as the model 1. Then the parameters p and q were added or decremented by 1, a plurality of candidate models were constructed, and the optimal model was filtered and recorded as the model 2. The model 1 and the model 2 were employed to predict the incidence rates of HFMD from July to December in 2015, and then compared them with the actual values. Mean absolute percentage error (MAPE), mean error rate (MER), mean square error (MSE), and mean absolute error (MAE) were used to evaluate the fitting and prediction effects of the two models. Results Model 1 was SARIMA(1,0,0)(1,1,0)₁₂. There were two models 2, including SARIMA(1,0,1)(1,1,0)₁₂ and SARIMA(1,0, 1) (0, 1, 1)₁₂. In the fitting phase, the MAPE fitted by the SARIMA(1,0,0)(1,1,0)₁₂, SARIMA(1,0,1)(1,1,0)₁₂ and SARIMA(1,0, 1)(0, 1, 1)₁₂ were 22.891%, 20.015% and 19.985%, respectively. The MAPE, MER, MSE and MAE predicted by the SARIMA(1,0,0)(1,1,0)₁₂, SARIMA(1,0,1)(1,1,0)₁₂ and SARIMA(1,0, 1) (0, 1, 1)₁₂ were 9.119%, 8.988%, 1.874 and 1.107; 11.000%, 10.909%, 2.552 and 1.344; 8.711%, 8.477%, 1.857 and 1.044, respectively. Conclusions SARIMA (1, 0, 1)(0, 1, 1)₁₂ is the best model, and its fitting and prediction effects are better than those of the SARIMA(1,0,0)(1,1,0)₁₂ model established by the graphic method. In the SARIMA modeling process, the approximate range of model parameters should be determined by the graphic method, and the optimal parameters should be screened by step-by-step methods to improve the accuracy of the model.