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Point and interval forecasts of mortality rates and life expectancy: A comparison of ten principal component methods

Author

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  • Han Lin Shang

    (Macquarie University)

  • Heather Booth

    (Australian National University)

  • Rob Hyndman

    (Monash University)

Abstract

Using the age- and sex-specific data of 14 developed countries, we compare the point and interval forecast accuracy and bias of ten principal component methods for forecasting mortality rates and life expectancy. The ten methods are variants and extensions of the Lee-Carter method. Based on one-step forecast errors, the weighted Hyndman-Ullah method provides the most accurate point forecasts of mortality rates and the Lee-Miller method is the least biased. For the accuracy and bias of life expectancy, the weighted Hyndman-Ullah method performs the best for female mortality and the Lee-Miller method for male mortality. While all methods underestimate variability in mortality rates, the more complex Hyndman-Ullah methods are more accurate than the simpler methods. The weighted Hyndman-Ullah method provides the most accurate interval forecasts for mortality rates, while the robust Hyndman-Ullah method provides the best interval forecast accuracy for life expectancy.

Suggested Citation

  • Han Lin Shang & Heather Booth & Rob Hyndman, 2011. "Point and interval forecasts of mortality rates and life expectancy: A comparison of ten principal component methods," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 25(5), pages 173-214.
  • Handle: RePEc:dem:demres:v:25:y:2011:i:5
    DOI: 10.4054/DemRes.2011.25.5
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    1. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2011. "Mortality density forecasts: An analysis of six stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 355-367, May.
    2. Hyndman, Rob J. & Khandakar, Yeasmin, 2008. "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i03).
    3. Booth, H. & Tickle, L., 2008. "Mortality Modelling and Forecasting: a Review of Methods," Annals of Actuarial Science, Cambridge University Press, vol. 3(1-2), pages 3-43, September.
    4. Ronald Lee & Timothy Miller, 2001. "Evaluating the performance of the lee-carter method for forecasting mortality," Demography, Springer;Population Association of America (PAA), vol. 38(4), pages 537-549, November.
    5. Shripad Tuljapurkar & Nan Li & Carl Boe, 2000. "A universal pattern of mortality decline in the G7 countries," Nature, Nature, vol. 405(6788), pages 789-792, June.
    6. Felipe, A. & Guillen, M. & Perez-Marin, A. M., 2002. "Recent Mortality Trends in the Spanish Population," British Actuarial Journal, Cambridge University Press, vol. 8(4), pages 757-786, October.
    7. Piet De Jong & Leonie Tickle, 2006. "Extending Lee-Carter Mortality Forecasting," Mathematical Population Studies, Taylor & Francis Journals, vol. 13(1), pages 1-18.
    8. Arthur Renshaw & Steven Haberman, 2003. "Lee–Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 119-137, January.
    9. Booth, Heather, 2006. "Demographic forecasting: 1980 to 2005 in review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 547-581.
    10. Heather Booth & Rob Hyndman & Leonie Tickle & Piet de Jong, 2006. "Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 15(9), pages 289-310.
    11. John Bongaarts, 2005. "Long-range trends in adult mortality: Models and projection methods," Demography, Springer;Population Association of America (PAA), vol. 42(1), pages 23-49, February.
    12. Bircan Erbas & Rob J. Hyndman & Dorota M. Gertig, 2005. "Forecasting age-specific breast cancer mortality using functional data models," Monash Econometrics and Business Statistics Working Papers 3/05, Monash University, Department of Econometrics and Business Statistics.
    13. Jeff Tayman & Stanley Smith & Jeffrey Lin, 2007. "Precision, bias, and uncertainty for state population forecasts: an exploratory analysis of time series models," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 26(3), pages 347-369, June.
    14. Dorina Lazar & Michel M. Denuit, 2009. "A multivariate time series approach to projected life tables," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 806-823, November.
    15. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    16. Renshaw, A.E. & Haberman, S., 2006. "A cohort-based extension to the Lee-Carter model for mortality reduction factors," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 556-570, June.
    17. Cairns, Andrew J. G., 2000. "A discussion of parameter and model uncertainty in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 27(3), pages 313-330, December.
    18. Hyndman, Rob J. & Booth, Heather, 2008. "Stochastic population forecasts using functional data models for mortality, fertility and migration," International Journal of Forecasting, Elsevier, vol. 24(3), pages 323-342.
    19. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    20. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
    21. Nico Keilman & Dinh Quang Pham & Arve Hetland, 2002. "Why population forecasts should be probabilistic - illustrated by the case of Norway," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 6(15), pages 409-454.
    22. Lawrence R. Carter & Alexia Prskawetz, 2001. "Examining structural shifts in mortality using the Lee-Carter method," MPIDR Working Papers WP-2001-007, Max Planck Institute for Demographic Research, Rostock, Germany.
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    More about this item

    Keywords

    forecasting; life expectancy; principal components analysis; Lee-Carter model; mortality forecasting; interval forecasts; forecasting time series;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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