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State space models for estimating and forecasting fertility

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  • Rueda, Cristina
  • Rodríguez, Pilar
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    Abstract

    We introduce multivariate state space models for estimating and forecasting fertility rates that are dynamic alternatives to logistic representations for fixed time points. Strategies are provided for the Kalman filter and for quasi-Newton algorithm initialization, that assure the convergence of the iterative fitting process. The broad impact of the new methodology in practice is shown using data series from Spain, Sweden and Australia, and by comparing the results with a recent approach based on functional data analysis and also with official forecasts. Very satisfactory short- and medium-term forecasts are obtained. Besides this, the new modeling proposal provides practitioners with several suitable interpretative tools, and the application here is an interesting example of the usefulness of the state space representation in modelling real multivariate processes.

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    Bibliographic Info

    Article provided by Elsevier in its journal International Journal of Forecasting.

    Volume (Year): 26 (2010)
    Issue (Month): 4 (October)
    Pages: 712-724

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    Handle: RePEc:eee:intfor:v:26:y::i:4:p:712-724

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    Web page: http://www.elsevier.com/locate/ijforecast

    Related research

    Keywords: State space model Kalman filter Fertility rates Demographic forecast Logistic model Total fertility rate;

    References

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    1. 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.
    2. Jan M. Hoem, 2005. "Why does Sweden have such high fertility?," MPIDR Working Papers WP-2005-009, Max Planck Institute for Demographic Research, Rostock, Germany.
    3. 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.
    4. FFF1Gunnar NNN1Andersson, 2004. "Childbearing Developments in Denmark, Norway, and Sweden from the 1970s to the 1990s: A Comparison," Demographic Research Special Collections, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 3(7), pages 155-176, April.
    5. Rob J Hyndman & Heather Booth, 2006. "Stochastic population forecasts using functional data models for mortality, fertility and migration," Monash Econometrics and Business Statistics Working Papers 14/06, Monash University, Department of Econometrics and Business Statistics.
    6. Jan M. Hoem, 2005. "Why does Sweden have such high fertility?," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 13(22), pages 559-572, November.
    7. 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.
    8. Evert Imhoff & Nico Keilman, 2000. "On the Quantum and Tempo of Fertility: Comment," Population and Development Review, The Population Council, Inc., vol. 26(3), pages 549-553.
    9. 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.
    10. Carl Schmertmann, 2003. "A system of model fertility schedules with graphically intuitive parameters," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 9(5), pages 81-110, October.
    11. Commandeur, Jacques J.F. & Koopman, Siem Jan, 2007. "An Introduction to State Space Time Series Analysis," OUP Catalogue, Oxford University Press, number 9780199228874.
    12. Booth, Heather, 2006. "Demographic forecasting: 1980 to 2005 in review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 547-581.
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