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Probabilistic forecasting using stochastic diffusion models, with applications to cohort processes of marriage and fertility

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  • Mikko Myrskylä

    (Max Planck Institute for Demographic Research, Rostock, Germany)

  • Joshua R. Goldstein

    (Max Planck Institute for Demographic Research, Rostock, Germany)

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    Abstract

    We study prediction and error propagation in Hernes, Gompertz, and logistic models for innovation diffusion. We develop a unifying framework in which the models are linearized with respect to cohort age and predictions are derived from the underlying linear process. We develop and compare methods for deriving the predictions and show how Monte Carlo simulation can be used to estimate prediction uncertainty for a wide class of underlying linear processes. For an important special case, random walk with, we develop an analytic prediction variance estimator. Both the Monte Carlo method and the analytic variance estimator allow the forecasters to make precise the level of within-model prediction uncertainty in innovation diffusion models. Empirical applications to first births, first marriages and cumulative fertility illustrate the usefulness of these methods.

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    File URL: http://www.demogr.mpg.de/papers/working/wp-2010-013.pdf
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    Bibliographic Info

    Paper provided by Max Planck Institute for Demographic Research, Rostock, Germany in its series MPIDR Working Papers with number WP-2010-013.

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    Length: 37 pages
    Date of creation: Feb 2010
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    Handle: RePEc:dem:wpaper:wp-2010-013

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    Web page: http://www.demogr.mpg.de/

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    1. Meade, Nigel & Islam, Towhidul, 2006. "Modelling and forecasting the diffusion of innovation - A 25-year review," International Journal of Forecasting, Elsevier, Elsevier, vol. 22(3), pages 519-545.
    2. Gruber, H. & Verboven, F.L., 1998. "The Diffusion of Mobile Telecommunications Services in the European Union," Discussion Paper, Tilburg University, Center for Economic Research 1998-138, Tilburg University, Center for Economic Research.
    3. Jan Hoem & Dan Madien & Jørgen Nielsen & Else-Marie Ohlsen & Hans Hansen & Bo Rennermalm, 1981. "Experiments in modelling recent Danish fertility curves," Demography, Springer, Springer, vol. 18(2), pages 231-244, May.
    4. Kohler, Hans-Peter, 2001. "Fertility and Social Interaction: An Economic Perspective," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780199244591, October.
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