﻿ SARIMA模型在长治市肺结核预测中的应用
 中国医科大学学报  2018, Vol. 47 Issue (7): 585-588

#### 文章信息

ZHANG Xihong, LI Hui, CAO Wenjun, CUI Yongmei
SARIMA模型在长治市肺结核预测中的应用
Application of the SARIMA Model in the Prediction of Pulmonary Tuberculosis in Changzhi City

Journal of China Medical University, 2018, 47(7): 585-588

### 文章历史

SARIMA模型在长治市肺结核预测中的应用

1. 长治医学院数学教研室, 山西 长治 046000;
2. 北京师范大学统计学院数理统计系, 北京 100875;
3. 长治医学院公共卫生与预防医学系流行病与卫生统计学教研室, 山西 长治 046000;
4. 长治市疾病预防控制中心传染病防控科, 山西 长治 046011

Application of the SARIMA Model in the Prediction of Pulmonary Tuberculosis in Changzhi City
1. Teaching and Research Section of Mathematics, Changzhi Medical College, Changzhi 046000, China;
2. Department of Mathematical Statistics, School of Statistics, Beijing Normal University, Beijing 100875, China;
3. Teaching and Research Section of Epidemiology and Health Statistics, Department of Public Health and Preventive Medicine, Changzhi Medical College, Changzhi 046000, China;
4. Department of Infectious Diseases Prevention and Control, Changzhi Center for Disease Control and Prevention, Changzhi 046011, China
Abstract: Objective To investigate the pattern of pulmonary tuberculosis in Changzhi city by using the time-series seasonal autoregressive integrated moving average(SARIMA) model to provide a reliable basis for the prevention and control of tuberculosis. Methods The monthly incidence of pulmonary tuberculosis in Changzhi city from January 2010 to December 2017 was collected. On the basis of this number, the SARIMA model was established using Eviews3.1. The established SARIMA model was used to predict the number of patients with pulmonary tuberculosis from July to December 2017 and compared with the actual numbers to evaluate the prediction effect of the model. In addition, the model was used to predict the incidence of tuberculosis in Changzhi city from January to December in 2018. Results The SARIMA model was finally established as SARIMA (2, 1, 0)×(1, 0, 1)12, with the expression of (1-B) (1+0.657B+0.279B2) (1-0.906B12)yt=(1-0.885B12) εt, yt=ln (xt), of which εt-WN (0, 0, 1272). The model was suitable for predicting the incidence of pulmonary tuberculosis in Changzhi city, with an average relative error of 5.96% for the predicted values from July to December 2017. Conclusion The time series model SARIMA(2, 1, 0)×(1, 0, 1)12 can better investigate the incidence of pulmonary tuberculosis in Changzhi and effectively predict the incidence of tuberculosis.

1 材料与方法 1.1 资料来源

1.2 方法

1.2.1

SARIMA模型简介：SARIMA（p，d，q）×（P，D，Q）S也叫乘积SARIMA模型，如果一个时间序列既有季节性又有趋势，适合建立的模型为SARIMA模型。构建SARIMA模型基本步骤为数据预处理、模型识别和定阶、模型参数估计和模型诊断、模型预测效果评价、预测。SARIMA模型的数学表达式为：

ϕ（B）Φ（BS）（1-B）d（1-BSDXt=θ（B）Θ（BSεt

ϕ（B）=1-ϕlB-…-ϕpBp

θ（B）=1-θlB-…-θqBq

Φ（BS）=1-ΦlBS-…-ΦpBPS

Θ（BS）=1-ΘlBS-…-ΘQBQS

t表示时间，Xt表示肺结核月发病人数，B表示滞后算子，εt是白噪声，ϕ（B）和Φ（B）满足平稳性条件，θ（B）和Θ（B）满足可逆性条件，即这4个多项式的根都在单位圆外。

1.2.2

1.2.3

1.2.4

1.2.5

1.2.6

2 结果 2.1 时间序列特征分析（图 1
 A, curve graph of number of patients; B, curve graph of the number of patients after logarithmic transformation. 图 1 2010年1月至2017年6月长治市肺结核病发病人数时序图 Fig.1 Sequence diagram of the number of patients with pulmonary tuberculosis in Changzhi from January 2010 to June 2017

2.2 ACF分析

 图 2 样本序列的ACF和PACF Fig.2 The ACF and PACF of the sample sequence

2.3 模型识别和检验

 图 3 新序列的ACF Fig.3 The ACF of the new sequence

（1-B）（1+0.657B+0.279B2）（1-0.906B12yt=（1-0.885B12εtyt=ln（xt

 图 4 SARIMA的估计结果 Fig.4 The estimated results of SARIMA

 图 5 残差序列的ACF和PACF Fig.5 The ACF and PACF of the residual sequence

2.4 模型预测效果评价

 Month Actual incidence（n） Predicted incidence（n） Absolute error Relative error（%） July 107 101 6 5.60 August 115 100 15 13.04 September 90 92 2 2.22 October 95 95 0 0.00 November 116 90 16 13.79 December 91 92 1 1.10

2.5 预测结果

3 讨论

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