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Robust forecasting of mortality and fertility rates: a functional data approach

  • Rob J. Hyndman

    ()

  • Md. Shahid Ullah

    ()

We propose a new method for forecasting age-specific mortality and fertility rates observed over time. Our approach allows for smooth functions of age, is robust for outlying years due to wars and epidemics, and provides a modelling framework that is easily adapted to allow for constraints and other information. We combine ideas from functional data analysis, nonparametric smoothing and robust statistics to form a methodology that is widely applicable to any functional time series data, and age-specific mortality and fertility in particular. We show that our model is a generalization of the Lee-Carter model commonly used in mortality and fertility forecasting. The methodology is applied to French mortality data and Australian fertility data, and we show that the forecasts obtained are superior to those from the Lee-Carter method and several of its variants.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2005/wp2-05.pdf
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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 2/05.

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Length: 24 pages
Date of creation: Feb 2005
Date of revision:
Handle: RePEc:msh:ebswps:2005-2
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Web page: http://www.buseco.monash.edu.au/depts/ebs/Email:


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  1. 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.
  2. N. Locantore & J. Marron & D. Simpson & N. Tripoli & J. Zhang & K. Cohen & Graciela Boente & Ricardo Fraiman & Babette Brumback & Christophe Croux & Jianqing Fan & Alois Kneip & John Marden & Daniel P, 1999. "Robust principal component analysis for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 8(1), pages 1-73, June.
  3. Hyndman, R.J. & Koehler, A.B. & Ord, J.K. & Snyder, R.D., 2001. "Prediction Intervals for Exponential Smoothing State Space Models," Monash Econometrics and Business Statistics Working Papers 11/01, Monash University, Department of Econometrics and Business Statistics.
  4. Hyndman, R.J. & Koehler, A.B. & Snyder, R.D. & Grose, S., 2000. "A State Space Framework for Automatic Forecasting Using Exponential Smoothing Methods," Monash Econometrics and Business Statistics Working Papers 9/00, Monash University, Department of Econometrics and Business Statistics.
  5. Croux, Christophe & Ruiz-Gazen, Anne, 2005. "High breakdown estimators for principal components: the projection-pursuit approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 206-226, July.
  6. repec:cup:cbooks:9780521785167 is not listed on IDEAS
  7. 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.
  8. 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.
  9. 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.
  10. Simon N. Wood, 2003. "Thin plate regression splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 95-114.
  11. repec:cup:cbooks:9780521780506 is not listed on IDEAS
  12. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
  13. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
  14. Lee, Ronald D., 1993. "Modeling and forecasting the time series of US fertility: Age distribution, range, and ultimate level," International Journal of Forecasting, Elsevier, vol. 9(2), pages 187-202, August.
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