SARIMA-GRNN组合模型在伤寒与副伤寒逐月发病数预测中的应用

李文豪; 曾昱兴; 李笑颜; 彭远舟; 张艳炜; 陈青山; 程锦泉

doi:10.16462/j.cnki.zhjbkz.2021.11.019

SARIMA-GRNN组合模型在伤寒与副伤寒逐月发病数预测中的应用

doi: 10.16462/j.cnki.zhjbkz.2021.11.019

1.
510630 广州，暨南大学基础医学与公共卫生学院流行病学教研室
2.
518000 深圳，中山大学公共卫生学院流行病与卫生统计学教研室
3.
518000 深圳，深圳市疾病预防与控制中心免疫规划所

基金项目:

国家“十三五”科技重大专项 2018ZX10715004

详细信息

通讯作者:
程锦泉，E-mail: cjinquan@szcdc.net

中图分类号: R135.2;R181.1
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- 文章访问数: 705
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- 被引次数: 0
出版历程
- 收稿日期: 2020-12-07
- 修回日期: 2021-05-20
- 网络出版日期: 2021-12-04
- 刊出日期: 2021-11-10

Application of SARIMA-GRNN combined model in forecasting the monthly incidence of typhoid fever and paratyphoid fever

1.
Department of Epidemiology, College of Basic Medicine and Public Health, Jinan University, Guangzhou 510630, China
2.
Department of Epidemiology and Statistics, College of Public Health, Sun Yat-sen University, Shenzhen 518000, China
3.
Institute of Immunization Program, Shenzhen Center for Disease Control and Prevention, Shenzhen 518000, China

Funds:

Major science and technology projects of the 13th Five-Year plan 2018ZX10715004

More Information

Corresponding author: CHENG Jin-quan, E-mail: cjinquan@szcdc.net

摘要

摘要: 目的建立季节性差分自回归移动平均(seasonal autoregressive integrated moving average, SARIMA)-广义回归神经网络(generalized regression neural network, GRNN)组合模型，为伤寒与副伤寒发病数的预测提供方法学上的新思路。方法利用2011年1月-2019年12月中国伤寒与副伤寒逐月发病数资料，分别构建SARIMA模型和SARIMA-GRNN组合模型，比较两种模型的拟合和预测效果。结果最优的SARIMA模型为SARIMA (2, 1, 1) (0, 1, 1)₁₂，SARIMA-GRNN组合模型的最优光滑因子(spread)为0.21。评价SARIMA-GRNN组合模型拟合效果的参数均方根误差(root mean squared error, RMSE)、平均绝对误差(mean absolute error, MAE)和平均绝对百分比误差(mean absolute percentage error, MAPE)为90.08、71.44和7.07%，分别小于SARIMA模型的99.44、79.15和7.86%；评价预测效果的RMSE、MAE和MAPE为100.86、75.94和9.57%，均小于SARIMA模型的125.44、97.33和10.89%。结论 SARIMA-GRNN组合模型比传统SARIMA模型更能拟合中国伤寒与副伤寒逐月的发病数，而且预测精度更高，可应用于伤寒与副伤寒逐月发病数的预测。
- 伤寒与副伤寒 /
- 季节性差分自回归移动平均模型 /
- 广义回归神经网络 /
- 组合模型
Abstract: Objective This study aimed to establish a seasonal autoregressive integrated moving average (SARIMA)-general regression neural network (GRNN) combined model, so as to provide new methodological ideas for forecasting the incidence of typhoid fever and paratyphoid fever. Methods Using data of typhoid fever and paratyphoid fever from January 2011 to December 2019, the SARIMA model and the SARIMA-GRNN combined model were constructed respectively, and the fitting and forecasting effects of the two models were compared. Results The optimal SARIMA model was SARIMA (2, 1, 1) (0, 1, 1)₁₂ and the optimal smoothing factor of SARIMA-GRNN combined model was 0.21. The root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) of the SARIMA-GRNN combined model fitting effect were 90.08, 71.44, and 7.07%, which were smaller than the SARIMA model's 99.44, 79.15, and 7.86% respectively. The RMSE, MAE, and MAPE of the forecasting effect were 100.86, 75.94, 9.57%, which were all smaller than 125.44, 97.33, 10.89% of the SARIMA model. Conclusions The SARIMA-GRNN combined model has a better fitting effect and higher forecasting effect than the traditional SARIMA model to forecast the monthly incidence of typhoid fever and paratyphoid fever in China. It can be used to predict the monthly incidence of typhoid fever and paratyphoid fever.
- Typhoid fever and paratyphoid fever /
- SARIMA Model /
- GRNN /
- Combined Model

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图 1 2011年1月-2018年12月中国伤寒与副伤寒发病数时间序列

Figure 1. Time series of typhoid and paratyphoid incidence in China from January 2011 to December 2018

下载: 全尺寸图片幻灯片

图 2 序列的自相关与偏自相关系数图

Figure 2. Autocorrelation function and Partial autocorrelation function graphs of time series

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图 3 SARIMA模型的预测值和实际值

Figure 3. The predicted value and the actual value of the SARIMA model

下载: 全尺寸图片幻灯片

图 4 不同光滑因子对应的均方根误差

Figure 4. Root mean square error of different spread

下载: 全尺寸图片幻灯片

图 5 SARIMA模型与SARIMA-GRNN模型拟合值和预测值的比较

Figure 5. Comparison of fitting value and forecast value between SARIMA model and SARIMA-GRNN model

下载: 全尺寸图片幻灯片

表 1 SARIMA (2, 1, 1) (0, 1, 1)₁₂模型参数显著性检验

Table 1. Significance test of the SARIMA (2, 1, 1) (0, 1, 1)₁₂ model parameters

模型	参数	标准差	t值	P值
ar1	-1.069 5	0.167 7	-6.377 4	< 0.001
ar2	-0.465 0	0.102 8	4.523 3	< 0.001
ma1	0.838 5	0.206 4	4.062 5	< 0.001
sma1	-0.999 9	0.331 8	-3.013 6	< 0.001

下载: 导出CSV

表 2 两种模型2019年逐月发病数的预测值及相对误差

Table 2. Forecast value and relative error of monthly incidence of two models in 2019

时间	实际值	SARIMA模型		SARIMA-GRNN模型
时间	实际值	预测值	相对误差(%)	预测值	相对误差(%)
2019年1月	702	653.19	6.95	681.62	2.90
2019年2月	502	502.73	0.15	626.55	24.81
2019年3月	591	631.55	6.86	669.97	13.36
2019年4月	1 000	754.62	24.54	779.69	22.03
2019年5月	950	1 146.91	20.73	1 067.44	12.36
2019年6月	1 000	1 078.38	7.84	1 015.80	1.58
2019年7月	1 102	1 336.12	21.25	1 274.82	15.68
2019年8月	1 040	1 127.72	8.43	1 050.82	1.04
2019年9月	881	967.54	9.82	937.11	6.37
2019年10月	806	816.81	1.34	836.96	3.84
2019年11月	642	569.49	11.29	648.61	1.03
2019年12月	571	505.46	11.48	627.53	9.90
注: 相对误差=(预测值-实际值)/实际值×100%。

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表 3 SARIMA模型与SARIMA-GRNN模型拟合和预测效果的比较

Table 3. Comparison of fitting and forecasting effects between SARIMA model and SARIMA-GRNN model

模型	拟合效果(2012-2018年)			预测效果(2019年)
模型	RMSE	MAE	MAPE(%)	RMSE	MAE	MAPE(%)
SARIMA	99.44	79.15	7.86	125.44	97.33	10.89
SARIMA-GRNN	90.08	71.44	7.07	100.86	75.94	9.57

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