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Stochastic population forecasts using functional data models for mortality, fertility and migration

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  • Rob J Hyndman

    ()

  • Heather Booth

Abstract

Age-sex-specific population forecasts are derived through stochastic population renewal using forecasts of mortality, fertility and net migration. Functional data models with time series coefficients are used to model age-specific mortality and fertility rates. As detailed migration data are lacking, net migration by age and sex is estimated as the difference between historic annual population data and successive populations one year ahead derived from a projection using fertility and mortality data. This estimate, which includes error, is also modeled using a functional data model. The three models involve different strengths of the general Box-Cox transformation chosen to minimise out-of-sample forecast error. Uncertainty is estimated from the model, with an adjustment to ensure the one-step-forecast variances are equal to those obtained with historical data. The three models are then used in the Monte Carlo simulation of future fertility, mortality and net migration, which are combined using the cohort-component method to obtain age-specific forecasts of the population by sex. The distribution of forecasts provides probabilistic prediction intervals. The method is demonstrated by making 20-year forecasts using Australian data for the period 1921-2003.

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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 14/06.

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Length: 34 pages
Date of creation: May 2006
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Handle: RePEc:msh:ebswps:2006-14

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Keywords: Fertility forecasting; functional data; mortality forecasting; net migration; nonparametric smoothing; population forecasting; principal components; simulation.;

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References

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  1. Renshaw, A. E. & Haberman, S., 2003. "Lee-Carter mortality forecasting with age-specific enhancement," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 255-272, October.
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  3. 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.
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  11. 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.
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  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.
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Citations

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Cited by:
  1. Leontine Alkema & Adrian Raftery & Patrick Gerland & Samuel Clark & François Pelletier & Thomas Buettner & Gerhard Heilig, 2011. "Probabilistic Projections of the Total Fertility Rate for All Countries," Demography, Springer, vol. 48(3), pages 815-839, August.
  2. 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.
  3. Gerard Keogh, 2013. "Modelling Asylum Migration Pull-Force Factors in the EU-15," The Economic and Social Review, Economic and Social Studies, vol. 44(3), pages 371–399.
  4. Shripad Tuljapurkar, 2006. "Population Forecasts, Fiscal Policy, and Risk," Economics Working Paper Archive wp_471, Levy Economics Institute.
  5. Han Lin Shang, 2012. "Point and interval forecasts of age-specific life expectancies," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 27(21), pages 593-644, November.
  6. 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.
  7. Han Lin Shang, 2010. "Nonparametric modeling and forecasting electricity demand: an empirical study," Monash Econometrics and Business Statistics Working Papers 19/10, Monash University, Department of Econometrics and Business Statistics.
  8. T. Gudaitis & A. Fiori Maccioni, 2014. "Optimal Individual Choice of Contribution to Second Pillar Pension System in Lithuania," Working Paper CRENoS 201402, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
  9. Rueda, Cristina & Rodríguez, Pilar, 2010. "State space models for estimating and forecasting fertility," International Journal of Forecasting, Elsevier, vol. 26(4), pages 712-724, October.
  10. 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.
  11. Shang, Han Lin, 2013. "Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 185-198.
  12. Shang, Han Lin & Hyndman, Rob.J., 2011. "Nonparametric time series forecasting with dynamic updating," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1310-1324.
  13. Alexander Dokumentov & Rob J Hyndman, 2013. "Two-dimensional smoothing of mortality rates," Monash Econometrics and Business Statistics Working Papers 26/13, Monash University, Department of Econometrics and Business Statistics.
  14. Andrés M. Alonso & Daniel Peña & Julio Rodríguez, 2008. "A methodology for population projections: an application to Spain," Statistics and Econometrics Working Papers ws084512, Universidad Carlos III, Departamento de Estadística y Econometría.
  15. Goia, Aldo & May, Caterina & Fusai, Gianluca, 2010. "Functional clustering and linear regression for peak load forecasting," International Journal of Forecasting, Elsevier, vol. 26(4), pages 700-711, October.
  16. Laurie Brown & Binod Nepal & Heather Booth & Sophie Pennec & Kaarin Anstey & Ann Harding, 2011. "Dynamic Modelling of Ageing and Health: The Dynopta Microsimulation Model," NATSEM Working Paper Series 11/14, University of Canberra, National Centre for Social and Economic Modelling.
  17. Han Lin Shang, 2012. "Point and interval forecasts of age-specific fertility rates: a comparison of functional principal component methods," Monash Econometrics and Business Statistics Working Papers 10/12, Monash University, Department of Econometrics and Business Statistics.
  18. A. Bitinas & A. Fiori Maccioni, 2013. "Lithuanian pension system’s reforms following demographic and social transitions," Working Paper CRENoS 201315, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.

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