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Coherent Mortality Forecasting: The Product-Ratio Method With Functional Time Series Models

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  • Rob Hyndman

    ()

  • Heather Booth

    ()

  • Farah Yasmeen

    ()

Abstract

When independence is assumed, forecasts of mortality for subpopulations are almost always divergent in the long term. We propose a method for coherent forecasting of mortality rates for two or more subpopulations, based on functional principal components models of simple and interpretable functions of rates. The product-ratio functional forecasting method models and forecasts the geometric mean of subpopulation rates and the ratio of subpopulation rates to product rates. Coherence is imposed by constraining the forecast ratio function through stationary time series models. The method is applied to sex-specific data for Sweden and state-specific data for Australia. Based on out-of-sample forecasts, the coherent forecasts are at least as accurate in overall terms as comparable independent forecasts, and forecast accuracy is homogenized across subpopulations. Copyright Population Association of America 2013

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Bibliographic Info

Article provided by Springer in its journal Demography.

Volume (Year): 50 (2013)
Issue (Month): 1 (February)
Pages: 261-283

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Handle: RePEc:spr:demogr:v:50:y:2013:i:1:p:261-283

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Web page: http://www.springer.com/economics/journal/13524

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Related research

Keywords: Mortality forecasting; Coherent forecasts; Functional data; Lee-Carter method; Life expectancy;

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References

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  1. Rob J. Hyndman & Han Lin Shang, 2008. "Rainbow plots, Bagplots and Boxplots for Functional Data," Monash Econometrics and Business Statistics Working Papers 9/08, Monash University, Department of Econometrics and Business Statistics.
  2. Han Lin Shang & Rob J Hyndman & Heather Booth, 2010. "A comparison of ten principal component methods for forecasting mortality rates," Monash Econometrics and Business Statistics Working Papers 8/10, Monash University, Department of Econometrics and Business Statistics.
  3. Rob J. Hyndman & Yeasmin Khandakar, . "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, American Statistical Association, vol. 27(i03).
  4. Ronald Lee & Timothy Miller, 2001. "Evaluating the performance of the lee-carter method for forecasting mortality," Demography, Springer, vol. 38(4), pages 537-549, November.
  5. 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.
  6. Heather Booth & Rob J Hyndman & Leonie Tickle & Piet de Jong, 2006. "Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions," Monash Econometrics and Business Statistics Working Papers 13/06, Monash University, Department of Econometrics and Business Statistics.
  7. 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, July.
  8. 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.
  9. Rob J Hyndman & Heather Booth & Farah Yasmeen, 2011. "Coherent Mortality Forecasting The Product-ratio Method with Functional Time Series Models," Working Papers 201116, ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales.
  10. Ortega, Jose Antonio & Poncela, Pilar, 2005. "Joint forecasts of Southern European fertility rates with non-stationary dynamic factor models," International Journal of Forecasting, Elsevier, vol. 21(3), pages 539-550.
  11. Kevin M. White, 2002. "Longevity Advances in High-Income Countries, 1955-96," Population and Development Review, The Population Council, Inc., vol. 28(1), pages 59-76.
  12. Nan Li & Ronald Lee, 2005. "Coherent mortality forecasts for a group of populations: An extension of the lee-carter method," Demography, Springer, vol. 42(3), pages 575-594, August.
  13. 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.
  14. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718.
  15. 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.
  16. 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.
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  1. > Econometrics > Forecasting
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Cited by:
  1. Rob J Hyndman & Heather Booth & Farah Yasmeen, 2011. "Coherent Mortality Forecasting The Product-ratio Method with Functional Time Series Models," Working Papers 201116, ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales.
  2. Lenny Stoeldraijer & Coen van Duin & L.J.G van Wissen & Fanny Janssen, 2013. "Impact of different mortality forecasting methods and explicit assumptions on projected future life expectancy: The case of the Netherlands," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 29(13), pages 323-354, August.
  3. Adrian Raftery & Nevena Lalic & Patrick Gerland, 2014. "Joint probabilistic projection of female and male life expectancy," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(27), pages 795-822, March.

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