The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

A study comparison of mortality projection using parametric and non-parametric model

모수와 비모수 모형을 활용한 사망률 예측 비교 연구

  • Kim, Soon-Young (Statistical Research Institute, Statistics Korea) ;
  • Oh, Jinho (Statistical Research Institute, Statistics Korea)
  • Received : 2017.07.20
  • Accepted : 2017.08.19
  • Published : 2017.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

The interest of Korean society and government on future demographic structures is increasing due to rapid aging. Korea's mortality rate is decreasing, but the declined gap is variable. In this study, we compare the Lee-Carter, Lee-Miller, Booth-Maindonald-Smith model and functional data model (FDM) as well as Coherent FDM using non-parametric smoothing technique. We are then examine a reasonable model for projecting on mortality declined rate trend in terms of accuracy of mortality rate by ages and life expectancy. The possibility of using non-parametric techniques for the prediction of mortality in Korea was also examined. Based on the analysis results, FDM and Coherent FDM, which uses the non-parametric technique and reflects the trend of recent data, are excellent. As a result, FDM and Coherent FDM are good fit, and predictability is also excellent assuming no significant future changes.

급속한 고령화로 인하여 미래의 인구와 인구구조에 관해 사회와 정부의 관심이 증가하고 있으며 우리나라의 사망률은 감소하고 있으나 감소폭은 변동적이다. 본 연구에서는 이를 고려할 수 있는 모형을 살펴보고자 LC 모형, LM 모형, BMS 모형 그리고 비모수평활 기법이 적용된 FDM과 Coherent FDM을 비교 분석하여 연령별 사망률과 기대수명 예측의 정확성 측면에서 남녀 사망률 개선 추이를 예측하는데 적합한 모형을 살펴보았다. 또한 우리나라 사망률 예측에 비모수 기법의 활용 가능성을 검토하였다. 분석 결과 최근 자료의 추세를 잘 반영하는 비모수기법을 활용한 인구통계모델인 FDM과 Coherent FDM의 예측력이 우수함을 알 수 있었다. 결과적으로 FDM과 Coherent FDM은 적합이 뛰어나고, 미래에 변화가 크지 않다면 예측력 또한 우수하다 볼 수 있을 것이다.

Keywords

References

  1. Box, G. E. P and Cox, D. R. (1964). An analysis of transformations, Journal of the Royal Statistical Society, Series B, 26, 211-252.
  2. Booth, H., Maindonald, J., and Smith, L. (2002). Applying Lee-Carter under conditions of variable mortality decline, Population Studies, 56, 325-336. https://doi.org/10.1080/00324720215935
  3. De Jong, P. and Tickle, L. (2006). Extending Lee-Carter mortality forecasting, Mathematical Population Studies, 13, 1-18. https://doi.org/10.1080/08898480500452109
  4. Hyndman, R. J. (2010). demography: Forecasting mortality, fertility, migration and population data, R package version 1.07. Contribution from Heather Booth and Leonie Tickle and John Maindonald.
  5. Hyndman, R. J. and Booth, H. (2008). Stochastic population forecasts using functional data models for mortality, fertility and migration, International Journal of Forecasting, 24, 323-342. https://doi.org/10.1016/j.ijforecast.2008.02.009
  6. Hyndman, R. J., Booth, H., and Yasmeen, F. (2013). Coherent mortality forecasting: the product-ratio method with functional time series models, Demography, 50, 261-283. https://doi.org/10.1007/s13524-012-0145-5
  7. Hyndman, R. J. and Khandakar, Y. (2008). Automatic time series forecasting: the forecast package for R, Journal of Statistical Software, 27, 1-22.
  8. Hyndman, R. J., Koehler, A. B., Ord, J. K., and Snyder, R. D. (2008). Forecasting with Exponential Smoothing: The State Space Approach, Springer, Berlin.
  9. Hyndman, R. J. and Ullah, S. (2007). Robust forecasting of mortality and fertility rates: a functional data approach, Computational Statistics & Data Analysis, 51, 4942-4956. https://doi.org/10.1016/j.csda.2006.07.028
  10. Jeong, S. and Kim, K. W. (2011). A comparison study for mortality forecasting models by average life expectancy, The Korean Journal of Applied Statistics, 24, 115-125. https://doi.org/10.5351/KJAS.2011.24.1.115
  11. Jung, K. N., Baek, J. S., and Kim, D. G. (2013). Comparison of mortality estimate and prediction by the period of time series data used, The Korean Journal of Applied Statistics, 26, 1019-1032. https://doi.org/10.5351/KJAS.2013.26.6.1019
  12. Kang, J. C., Lee, D. S. and Shung, J. H. (2006). A study on the methodds for forecasting mortality considering longevity risk, The Journal of Risk Management, 17, 153-178.
  13. KOSIS (2016). Population Projections (2015-2065).
  14. Lee, R. D. and Carter, L. R. (1992). Modeling and forecasting U.S. mortality, Journal of the American Statistical Association, 87, 659-671.
  15. Lee, R. D. and Miller, T. (2001). Evaluating the performance of the Lee-Carter method for forecasting mortality, Demography, 38, 537-549. https://doi.org/10.1353/dem.2001.0036
  16. Li, N. and Lee R. (2005). Coherent mortality forecasts for a group of populations: an extension of the Lee-Carter method, Demography, 42, 575-594 https://doi.org/10.1353/dem.2005.0021
  17. Li, N., Lee, R. and Gerland, P. (2013). Extending the Lee-Carter method to model the rotation of age patterns of mortality decline for long-term projections, Demography, 50, 2037-2051. https://doi.org/10.1007/s13524-013-0232-2
  18. Park, Y. S., Kim, K. W., Lee, D. H., and Lee, Y. K. (2005). A comparison of two models for forecasting mortality in South Korea, The Korean Journal of Applied Statistics, 18, 639-654. https://doi.org/10.5351/KJAS.2005.18.3.639
  19. Ramsay, J. O. and Silverman, B. W. (2005). Functional Data Analysis (2nd ed.), Springer, New York.
  20. Smith, S. K., Tayman, J., and Swanson, D. A. (2001). State and Local Population Projections: Methodology and Analysis, Kluwer Academic / Plenum Publishers, New York.
  21. Wood, S. N. (2003). Thin plate regression splines, Journal of the Royal Statistical Society, Series B, 65, 95-114. https://doi.org/10.1111/1467-9868.00374