Mortality Prediction and Application Based on APC Model

Hongmin Xiao; Haifei Ma; Hongyu Zhao

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Mortality Prediction and Application Based on APC Model

Hongmin Xiao, Haifei Ma, Hongyu Zhao

Published in Asia-Pacific Journal of Mathematics and Statistics (Volume 2, Issue 2)

Received: 24 March 2020 Accepted: 13 September 2020 Published: 23 September 2020

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Abstract

In this paper, the APC (age period cohort) model with year of birth effect is used to fit and predict China's population mortality data. Firstly, the parameters of APC model are estimated by maximum likelihood method. Through residual analysis of the model, it is found that the model captures the effects of age, calendar year and birth year, and the data fitting effect is good. Then the ARIMA time series model is used to fit the time index and the birth year index of the mortality model. The optimal ARIMA model is selected by AICc value for prediction, and then the predicted value of mortality rate is obtained, and the prediction effect is compared according to the real value of mortality. Finally, the life expectancy of population is predicted by using the predicted mortality value, and part of the age life expectancy table is drawn. The results show that: from the perspective of fitting effect and prediction effect, APC model is suitable for predicting China's population mortality rate. At the same time, we find that China's population life expectancy tends to be gradually extended, and the aging problem is becoming increasingly serious, which will bring huge financial pressure to China's life insurance enterprises and pension institutions.

Published in	Asia-Pacific Journal of Mathematics and Statistics (Volume 2, Issue 2)
Page(s)	5-9
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

APC Model, Residual Analysis, ARIMA Model,Life Expectancy

References

[1]	Lee R D, Carter L R. Modeling and forecasting US mortality [J]. Journal of American Statistical Association, 1992,87(14):659-675.
[2]	Renshaw A E, Haberman S. A cohort-based extension to the Lee-Carter model for mortality reduction factors[J]. Insurance: Mathematics and Economics, 2006,38(3): 556-570.
[3]	Currie I D, Durban M, Eilers P H C. Generalized linear array models with applications to multidimensional smoothing[J]. Journal of the Royal Statistical Society, 2006,68(2):259-280.
[4]	Steven Haberman, Arthur Renshaw. On age-period-cohort parametric mortality rate projections[J]. Insurance Mathematics and Economics, 2009,45(2):255-270.
[5]	Brouhns N, Denuit M, Vermunt J. A Poisson log-linear regression approach to the construction of projected lifetables[J]. Insurance: Mathematics and Economics,2002,31(3):373-393.
[6]	Cairns A J G, Blake D, Dowd K, et al. Mortality density forecasts: An analysis of six stochastic mortality models [J]. Social Science Electronic Publishing, 2011, 48( 3): 355-367.
[7]	Li N, Lee R, Gerland P. Extending the Lee-Carter Method to Model the Rotation of Age Patterns of Mortality Decline for Long-Term Projections[J]. Demography, 2013,50(6):2037-2051.
[8]	李志生,刘恒甲.Lee-Carter的估计与应用——基于中国人口数据的分析[J].中国人口科学,2010(3):47-56。
[9]	黄顺林,王晓军.加入出生年效应的死亡率预测及其在年金系数估计中的应用[J].统计与信息论坛,2010(05):81-86
[10]	韩猛,王晓军.Lee-Carter模型在中国城市人口死亡率预测中的应用与改进[J].保险研究,2010,(10): 3-9。
[11]	王晓军,任文东.有限数据下Lee-Carter模型在人口死亡率预测中的应用[J].统计研究,2012,(6):87-94。
[12]	杨泽祥,赵萍,王欣.人口生命表编制的一种新方法:死亡结构法[J].统计与决策,2014(01):4-7
[13]	苏晶晶,彭非.年龄-时期-队列模型参数估计方法最新研究进展[J].统计与决策,2014(23):21-26。
[14]	曾燕,陈曦,邓颖璐.创新的动态人口死亡率预测及其应用[J].系统工程理论与实践,2016,36(7):1710-1718。
[15]	曹园.基于Lee-Carter模型的我国死亡率预测[J].统计与决策,2018(9):32-36。
[16]	樊毅,张宁.基于全人口死亡率数据的随机死亡率模型拟合效果比较[J].统计与决策,2018(23):33-37。
[17]	王晓军,路倩.高龄人口死亡率预测模型的比较与选择[J].保险研究,2019(3):82-102。

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APA Style

Hongmin Xiao, Haifei Ma, Hongyu Zhao. (2020). Mortality Prediction and Application Based on APC Model. Asia-Pacific Journal of Mathematics and Statistics, 2(2), 5-9.

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ACS Style

Hongmin Xiao; Haifei Ma; Hongyu Zhao. Mortality Prediction and Application Based on APC Model. Asia-Pac. J. Math. Stat. 2020, 2(2), 5-9.

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AMA Style

Hongmin Xiao, Haifei Ma, Hongyu Zhao. Mortality Prediction and Application Based on APC Model. Asia-Pac J Math Stat. 2020;2(2):5-9.

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@article{10047502,
  author = {Hongmin Xiao and Haifei Ma and Hongyu Zhao},
  title = {Mortality Prediction and Application Based on APC Model},
  journal = {Asia-Pacific Journal of Mathematics and Statistics},
  volume = {2},
  number = {2},
  pages = {5-9},
  url = {https://www.sciencepublishinggroup.com/article/10047502},
  abstract = {In this paper, the APC (age period cohort) model with year of birth effect is used to fit and predict China's population mortality data. Firstly, the parameters of APC model are estimated by maximum likelihood method. Through residual analysis of the model, it is found that the model captures the effects of age, calendar year and birth year, and the data fitting effect is good. Then the ARIMA time series model is used to fit the time index and the birth year index of the mortality model. The optimal ARIMA model is selected by AICc value for prediction, and then the predicted value of mortality rate is obtained, and the prediction effect is compared according to the real value of mortality. Finally, the life expectancy of population is predicted by using the predicted mortality value, and part of the age life expectancy table is drawn. The results show that: from the perspective of fitting effect and prediction effect, APC model is suitable for predicting China's population mortality rate. At the same time, we find that China's population life expectancy tends to be gradually extended, and the aging problem is becoming increasingly serious, which will bring huge financial pressure to China's life insurance enterprises and pension institutions.},
 year = {2020}
}

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TY  - JOUR
T1  - Mortality Prediction and Application Based on APC Model
AU  - Hongmin Xiao
AU  - Haifei Ma
AU  - Hongyu Zhao
Y1  - 2020/09/23
PY  - 2020
T2  - Asia-Pacific Journal of Mathematics and Statistics
JF  - Asia-Pacific Journal of Mathematics and Statistics
JO  - Asia-Pacific Journal of Mathematics and Statistics
SP  - 5
EP  - 9
PB  - Science Publishing Group
UR  - http://www.sciencepg.com/article/10047502
AB  - In this paper, the APC (age period cohort) model with year of birth effect is used to fit and predict China's population mortality data. Firstly, the parameters of APC model are estimated by maximum likelihood method. Through residual analysis of the model, it is found that the model captures the effects of age, calendar year and birth year, and the data fitting effect is good. Then the ARIMA time series model is used to fit the time index and the birth year index of the mortality model. The optimal ARIMA model is selected by AICc value for prediction, and then the predicted value of mortality rate is obtained, and the prediction effect is compared according to the real value of mortality. Finally, the life expectancy of population is predicted by using the predicted mortality value, and part of the age life expectancy table is drawn. The results show that: from the perspective of fitting effect and prediction effect, APC model is suitable for predicting China's population mortality rate. At the same time, we find that China's population life expectancy tends to be gradually extended, and the aging problem is becoming increasingly serious, which will bring huge financial pressure to China's life insurance enterprises and pension institutions.
VL  - 2
IS  - 2
ER  -

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Author Information

Hongmin Xiao

Department of Mathematics, Northwest Normal University, Lanzhou, China
Haifei Ma

Department of Mathematics, Northwest Normal University, Lanzhou, China
Hongyu Zhao

Department of Mathematics, Northwest Normal University, Lanzhou, China

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Plain Text BibTeX RIS

APA Style

Hongmin Xiao, Haifei Ma, Hongyu Zhao. (2020). Mortality Prediction and Application Based on APC Model. Asia-Pacific Journal of Mathematics and Statistics, 2(2), 5-9.

Copy | Download

ACS Style

Hongmin Xiao; Haifei Ma; Hongyu Zhao. Mortality Prediction and Application Based on APC Model. Asia-Pac. J. Math. Stat. 2020, 2(2), 5-9.

Copy | Download

AMA Style

Hongmin Xiao, Haifei Ma, Hongyu Zhao. Mortality Prediction and Application Based on APC Model. Asia-Pac J Math Stat. 2020;2(2):5-9.

Copy | Download

@article{10047502,
  author = {Hongmin Xiao and Haifei Ma and Hongyu Zhao},
  title = {Mortality Prediction and Application Based on APC Model},
  journal = {Asia-Pacific Journal of Mathematics and Statistics},
  volume = {2},
  number = {2},
  pages = {5-9},
  url = {https://www.sciencepublishinggroup.com/article/10047502},
  abstract = {In this paper, the APC (age period cohort) model with year of birth effect is used to fit and predict China's population mortality data. Firstly, the parameters of APC model are estimated by maximum likelihood method. Through residual analysis of the model, it is found that the model captures the effects of age, calendar year and birth year, and the data fitting effect is good. Then the ARIMA time series model is used to fit the time index and the birth year index of the mortality model. The optimal ARIMA model is selected by AICc value for prediction, and then the predicted value of mortality rate is obtained, and the prediction effect is compared according to the real value of mortality. Finally, the life expectancy of population is predicted by using the predicted mortality value, and part of the age life expectancy table is drawn. The results show that: from the perspective of fitting effect and prediction effect, APC model is suitable for predicting China's population mortality rate. At the same time, we find that China's population life expectancy tends to be gradually extended, and the aging problem is becoming increasingly serious, which will bring huge financial pressure to China's life insurance enterprises and pension institutions.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Mortality Prediction and Application Based on APC Model
AU  - Hongmin Xiao
AU  - Haifei Ma
AU  - Hongyu Zhao
Y1  - 2020/09/23
PY  - 2020
T2  - Asia-Pacific Journal of Mathematics and Statistics
JF  - Asia-Pacific Journal of Mathematics and Statistics
JO  - Asia-Pacific Journal of Mathematics and Statistics
SP  - 5
EP  - 9
PB  - Science Publishing Group
UR  - http://www.sciencepg.com/article/10047502
AB  - In this paper, the APC (age period cohort) model with year of birth effect is used to fit and predict China's population mortality data. Firstly, the parameters of APC model are estimated by maximum likelihood method. Through residual analysis of the model, it is found that the model captures the effects of age, calendar year and birth year, and the data fitting effect is good. Then the ARIMA time series model is used to fit the time index and the birth year index of the mortality model. The optimal ARIMA model is selected by AICc value for prediction, and then the predicted value of mortality rate is obtained, and the prediction effect is compared according to the real value of mortality. Finally, the life expectancy of population is predicted by using the predicted mortality value, and part of the age life expectancy table is drawn. The results show that: from the perspective of fitting effect and prediction effect, APC model is suitable for predicting China's population mortality rate. At the same time, we find that China's population life expectancy tends to be gradually extended, and the aging problem is becoming increasingly serious, which will bring huge financial pressure to China's life insurance enterprises and pension institutions.
VL  - 2
IS  - 2
ER  -

Copy | Download