残差自回归模型和Holt双参数指数平滑模型在“一带一路”沿线部分国家婴儿死亡率预测中的应用及比较

李刚刚; 周秀芳; 白亚娜; 周莉; 韩晓丽; 任晓卫

doi:10.16462/j.cnki.zhjbkz.2019.01.019

残差自回归模型和Holt双参数指数平滑模型在“一带一路”沿线部分国家婴儿死亡率预测中的应用及比较

doi: 10.16462/j.cnki.zhjbkz.2019.01.019

1.
730000 兰州, 兰州大学公共卫生学院流行病与卫生统计学研究所
2.
730000 兰州, 兰州市妇幼保健院新生儿科

基金项目:

兰州市科技局兰州市新生儿出生队列研究项目 Science and Technology Bureau Newborn Birth Cohort Research Project, Lanzhou

"一带一路"重大专项 Major project of the Belt and Road, Lanzhou University

详细信息

通讯作者:
任晓卫, E-mail: renxw@lzu.edu.cn

中图分类号: R181
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- 被引次数: 0
出版历程
- 收稿日期: 2018-07-05
- 修回日期: 2018-10-06
- 刊出日期: 2019-01-10

Application and comparison of residual autoregressive model and Holt's two-parameter exponential smoothing model in infant mortality prediction in some countries along the Belt and Road Initiative

1.
Institute of Epidemiology and Health Statistics, School of Public Health, Lanzhou University, Lanzhou 730000, China
2.
Women and Children's Hospital of Lanzhou, Neonatology, Lanzhou 730000, China

Funds:

2015-RC-33 Science and Technology Bureau Newborn Birth Cohort Research Project, Lanzhou

2018ldbrzd008 Major project of the Belt and Road, Lanzhou University

More Information

Corresponding author: REN Xiao-wei, E-mail: renxw@lzu.edu.cn

摘要

摘要: 目的探讨残差自回归模型和Holt双参数指数平滑模型在"一带一路"沿线部分国家（中国-中南半岛经济走廊沿线）婴儿死亡率预测中的应用。方法利用越南、老挝、柬埔寨、缅甸、泰国、新加坡、马来西亚和中国1978-2013年婴儿死亡率时间序列数据作为训练集建立残差自回归模型、Holt双参数指数模型，以2014-2016年婴儿死亡率作为验证集验证模型，并比较拟合及预测效果。结果在各国婴儿死亡率预测模型拟合中，残差自回归模型各赤池信息准则（Akaike information criterion，AIC）评价指标均优于Holt双参数指数模型。预测方面两模型均显示出较高的预测精度，残差自回归预测模型大部分指标（绝对误差和相对误差）小于Holt双参数指数模型。其中老挝、缅甸、柬埔寨三个国家残差自回归模型对不同年份的婴儿死亡率（infant mortality rate，IMR）预测效果均优于Holt双参数指数模型。结论残差自回归模型和Holt双参数指数模型在"一带一路"沿线部分国家婴儿死亡率预测中表现均较好。残差自回归模型的拟合效果更优，残差自回归模型对婴儿死亡率的预测效果在大多数国家大多数年份优于Holt双参数指数模型。
- 一带一路 /
- 时间序列分析 /
- 婴儿死亡率 /
- 残差自回归模型 /
- Holt双参数指数模型
Abstract: Objective To explore the application of residual autoregressive model and Holt's two-parameter exponential model in the prediction of infant mortality rate in some countries along the "Belt and Road" (China-Indo-China Peninsula Economic Corridor). Methods The time series data of infant mortality rate in Vietnam, Laos, Cambodia, Myanmar, Thailand, Singapore, Malaysia, and China for 1978-2013 were used as training set to fit residual autoregressive model and Holt's two-parameter exponential model. The 2014-2016 data was used as the validation set to compare the performance of model prediction. Results The akaike information criterion (AIC) value of the residual autoregressive model was superior to Holt's two-parameter exponential model. Both prediction models showed high accuracy, and most evaluation indicators (absolute error and relative error) of residual autoregressive prediction model were smaller than Holt's two-parameter exponential model. The residual autoregressive models of Laos, Myanmar and Cambodia were better than the Holt's two-parameter exponential model for the infant mortality rate(IMR) prediction in different years. Conclusions The residual autoregressive model and Holt's two-parameter exponential model performed well in infant mortality rate prediction in some countries along the China-Indo-china Peninsula Economic Corridor. The residual autoregressive model has better fitting effect. The residual autoregressive model for infant mortality prediction is superior to the Holt two-parameter exponential model in most countries in most years.
- Belt and Road /
- Time series analysis /
- Infant mortality rate /
- Residual autoregressive model /
- Holt's two-parameter exponential mode

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图 1 1978-2013年中国-中南半岛经济走廊沿线八个国家婴儿死亡率时序图

Figure 1. Timing diagram of infant mortality in eight countries along the China-Indochina Economic Corridor from 1978 to 2013

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表 1 1978-2013年中国-中南半岛经济走廊沿线国家IMR序列检验结果

Table 1. Tests results of IMR in eight countries along the China-Indochina Economic Corridor from 1978 to 2013

国家	平稳性检验			纯随机性检验
国家	Dickey- Fuller	Lag order	P值	χ²值	v	P值
LA	-0.554	3	0.973	33.255	1	<0.001
MMR	-3.042	3	0.168	32.346	1	<0.001
KHM	-2.872	3	0.234	28.289	1	<0.001
VNM	-2.108	3	0.531	34.117	1	<0.001
CHN	-2.553	3	0.358	32.565	1	<0.001
TH	-0.585	3	0.971	32.642	1	<0.001
MYS	-0.928	3	0.935	31.454	1	<0.001
SGP	-1.682	3	0.697	33.381	1	<0.001

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表 2 各国IMR序列确定性趋势模型拟合效果

Table 2. Fitting effect of deterministic trend model of IMR in eight countries

国家	关于时间t的幂函数						关于历史观测值的函数
国家	AIC	R²	RMSE	MAE	DW	P值	AIC	R²	RMSE	MAE	Durbin h	P值
LA	-139.997 6	0.988 5	0.031 9	0.028 0	0.035 1	<0.001	-299.523 9	0.999 9	0.003 1	0.002 5	4.516 5	<0.001
MMR	-147.271 4	0.985 3	0.028 8	0.023 9	0.450 1	<0.001	-174.212 5	0.993 4	0.018 4	0.006 0	-2.825 0	0.002
KHM	-27.044 5	0.837 0	0.152 9	0.130 9	0.061 7	<0.001	-129.765 8	0.990 4	0.034 8	0.028 9	5.380 6	<0.001
VNM	-112.872 3	0.981 5	0.046 4	0.041 2	0.076 4	<0.001	-203.144 7	0.998 7	0.012 2	0.011 2	5.411 5	<0.001
CHN	-22.748 6	0.878 2	0.162 3	0.146 9	0.033 7	<0.001	-178.299 5	0.998 4	0.017 4	0.014 6	5.273 8	<0.001
TH	-207.907 0	0.999 3	0.012 4	0.010 4	0.139 9	<0.001	-275.442 2	0.999 9	0.004 3	0.003 6	4.216 5	<0.001
MYS	-63.792 1	0.962 6	0.091 8	0.073 2	0.079 1	<0.001	-171.495 2	0.998 4	0.019 2	0.012 8	4.342 5	<0.001
SGP	-44.508 9	0.962 2	0.120 0	0.104 0	0.078 7	<0.001	-136.956 1	0.997 4	0.031 4	0.026 1	3.305 9	<0.001

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表 3 各国IMR残差自回归模型拟合结果

Table 3. Results of autoregressive model fitting of IMR residual in eight countries

国家	残差自回归模型	AIC	RMSE	MAE
LA	x_t =1.010 8 x_t-1+ε_t ε_t=-0.932 6ε_t-1+a_t	-354.215 2	0.001 5	0.001 0
MMR	x_t =1.009 1 x_t-1+ε_t ε_t=0.413 9ε_t-1+a_t	-180.379 8	0.017 8	0.008 5
KHM	x_t =1.015 9 x_t-1+ε_t ε_t=-1.331 4εt-1+0.454 9ε_t-3+a_t	-250.583 3	0.006 1	0.004 7
VNM	x_t =1.007 8 x_t-1+ε_t ε_t=-1.087 3ε_t-1+0.207 8ε_t-5+a_t	-285.414 0	0.003 8	0.002 6
CHN	x_t =0.147 1+1.055 9 x_t-1+ε_t ε_t=-1.076 8ε_t-1+0.284 0ε_t-5+a_t	-284.738 4	0.003 6	0.002 6
TH	x_t =-0.053 9+0.996 7 x_t-1+ε_t ε_t=-0.765 6ε_t-1+a_t	-303.797 6	0.003 0	0.002 2
MYS	x_t =-0.223 1+0.957 9 x_t-1+ε_t ε_t=-0.809 1ε_t-1+a_t	-206.533 0	0.012 0	0.008 0
SGP	x_t =1.008 5 x_t-1+ε_t ε_t=-0.696 2ε_t-1+a_t	-153.444 7	0.026 0	0.019 9

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表 4 各国IMR序列Holt双参数指数模型拟合结果

Table 4. The results of Holt two-parameter exponential model for IMR in eight countries

国家	Holt双参数模型	AIC	RMSE	MAE
LA	S_t =0.903 6x_t+0.096 4(S_t-1+b_t-1)	-335.953 1	0.001 4	0.001 0
	b_t =0.903 6(S_t-S_t-1)+0.096 4b_t-1	-335.953 1	0.001 4	0.001 0
MMR	S_t =0.308 2x_t+0.691 8(S_t-1+b_t-1)	-153.728 7	0.017 1	0.008 6
	b_t =0.186 3(S_t-S_t-1)+0.813 7b_t-1	-153.728 7	0.017 1	0.008 6
KHM	S_t =0.999 9x_t+0.000 1(S_t-1+b_t-1)	-192.985 7	0.009 9	0.007 1
	b_t =0.999 9(S_t-S_t-1)+0.000 1b_t-1	-192.985 7	0.009 9	0.007 1
VNM	S_t =0.903 5x_t+0.096 5(S_t-1+b_t-1)	-260.680 5	0.003 9	0.002 7
	b_t =0.903 5(S_t-S_t-1)+0.096 5b_t-1	-260.680 5	0.003 9	0.002 7
CHN	S_t =0.999 9x_t+0.000 1(S_t-1+b_t-1)	-234.062 3	0.005 6	0.004 7
	b_t =0.999 9(S_t-S_t-1)+0.000 1b_t-1	-234.062 3	0.005 6	0.004 7
TH	S_t =0.905 7x_t+0.094 3(S_t-1+b_t-1)	-283.571 7	0.002 8	0.002 1
	b_t =0.759 4(S_t-S_t-1)+0.240 6b_t-1	-283.571 7	0.002 8	0.002 1
MYS	S_t =0.884 8x_t+0.115 2(S_t-1+b_t-1)	-181.615 4	0.011 6	0.008 5
	b_t =0.884 8(S_t-S_t-1)+0.115 2b_t-1	-181.615 4	0.011 6	0.008 5
SGP	S_t =0.999 9x_t+0.000 1(S_t-1+b_t-1)	-125.732 7	0.025 3	0.018 7
	b_t =0.999 9(S_t-S_t-1)+0.000 1b_t-1	-125.732 7	0.025 3	0.018 7
注：各序列模型均为ETS(A^a, A^b, N^c)，其中^a误差项，^b趋势项，^c季节项，A-相加模型、M-相乘模型、N-无和Z-自动选择。

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表 5 中国—中南半岛经济走廊沿线国家IMR序列模型预测结果

Table 5. Prediction results of IMR along the China-Indochina Peninsula Economic Corridor

国家	年份	实际值(‰)	预测(95% CI)值(‰)		绝对误差		相对误差(%)
国家	年份	实际值(‰)	残差自回归模型	Holt双参数模型	残差自回归模型	Holt双参数模型	残差自回归模型	Holt双参数模型
LA	2014	51.90	52.00(51.83~52.17)	52.02(51.88~52.16)	0.100 1	0.121 5	0.19	0.23
	2015	50.40	50.40(50.27~50.54)	50.38(50.24~50.52)	0.004 7	0.017 6	0.01	0.03
	2016	48.90	48.91(48.76~49.07)	48.93(48.80~49.06)	0.014 1	0.028 4	0.03	0.06
MMR	2014	42.80	42.77(41.21~44.38)	42.60(41.19~44.06)	0.034 3	0.201 0	0.08	0.47
	2015	41.40	41.27(39.79~42.80)	41.03(39.69~42.41)	0.132 5	0.373 8	0.32	0.90
	2016	40.10	39.88(38.47~41.34)	39.69(38.41~41.02)	0.218 4	0.406 3	0.54	1.01
KHM	2014	28.90	28.79(28.41~29.17)	28.63(28.08~29.20)	0.114 4	0.265 2	0.40	0.92
	2015	27.50	27.49(27.13~27.85)	27.29(26.77~27.83)	0.014 3	0.205 6	0.05	0.75
	2016	26.30	26.35(26.01~26.69)	26.17(25.67~26.68)	0.048 9	0.132 3	0.19	0.50
VNM	2014	17.80	17.77(17.63~17.92)	17.80(17.67~17.94)	0.025 7	0.004 9	0.14	0.03
	2015	17.60	17.60(17.49~17.72)	17.60(17.47~17.74)	0.004 0	0.002 8	0.02	0.02
	2016	17.30	17.36(17.25~17.47)	17.40(17.27~17.53)	0.059 6	0.102 3	0.34	0.59
CHN	2014	9.90	9.85(9.76~9.93)	9.87(9.76~9.98)	0.052 4	0.029 3	0.53	0.30
	2015	9.20	9.15(9.07~9.23)	9.16(9.06~9.26)	0.048 1	0.040 2	0.52	0.44
	2016	8.50	8.53(8.46~8.60)	8.55(8.45~8.64)	0.029 4	0.048 2	0.35	0.57
TH	2014	11.20	11.20(11.13~11.27)	11.22(11.16~11.28)	0.000 5	0.019 5	0.00	0.17
	2015	10.80	10.81(10.74~10.87)	10.82(10.76~10.88)	0.005 7	0.018 5	0.05	0.17
	2016	10.50	10.42(10.35~10.49)	10.42(10.36~10.48)	0.083 5	0.081 5	0.79	0.78
MYS	2014	6.90	6.95(6.78~7.13)	6.97(6.82~7.14)	0.053 2	0.074 7	0.77	1.08
	2015	7.00	6.91(6.75~7.07)	6.93(6.78~7.09)	0.088 3	0.068 5	1.26	0.98
	2016	7.10	7.07(6.89~7.24)	7.07(6.91~7.23)	0.033 7	0.027 6	0.47	0.39
SGP	2014	2.10	2.02(1.91~2.13)	2.04(1.94~2.15)	0.080 6	0.058 1	3.84	2.77
	2015	2.10	2.08(1.97~2.19)	2.07(1.97~2.18)	0.022 1	0.025 8	1.05	1.23
	2016	2.20	2.09(1.97~2.21)	2.09(1.98~2.19)	0.112 5	0.114 9	5.11	5.22

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