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Five different distributions for the Lee–Carter model of mortality forecasting: A comparison using GAS models

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  • Neves, César
  • Fernandes, Cristiano
  • Hoeltgebaum, Henrique

Abstract

This paper extends the well-known Lee–Carter model used for forecasting mortality rates by utilizing a new class of time series models, known as Generalized Autoregressive Score (GAS) or Dynamic Conditional Score (DCS) models. This framework can be used to derive a wide range of non-Gaussian time series models with time varying coefficients and has shown to be very successful in financial applications. In this paper we propose five probability models (Poisson, binomial, negative binomial, Gaussian and beta) based on the GAS framework to estimate the Lee–Carter parameters and dynamically forecast the mortality rates using a single unified step. The models are applied to the mortality rates time series for the male population of the United States, Sweden, Japan and the UK. Diagnostic tests are performed on quantile residuals, model selection is made via AIC and predictive accuracy of the models is compared using the Diebold–Mariano test. We conclude that, amongst the proposed models, the negative binomial extension of the Lee–Carter model is the most appropriate for forecasting mortality rates.

Suggested Citation

  • Neves, César & Fernandes, Cristiano & Hoeltgebaum, Henrique, 2017. "Five different distributions for the Lee–Carter model of mortality forecasting: A comparison using GAS models," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 48-57.
    • Handle: RePEc:eee:insuma:v:75:y:2017:i:c:p:48-57
    DOI: 10.1016/j.insmatheco.2017.04.004
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    Cited by:

    1. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    2. Nurul Aityqah Yaacob & Jamil J. Jaber & Dharini Pathmanathan & Sadam Alwadi & Ibrahim Mohamed, 2021. "Hybrid of the Lee-Carter Model with Maximum Overlap Discrete Wavelet Transform Filters in Forecasting Mortality Rates," Mathematics, MDPI, vol. 9(18), pages 1-11, September.
    3. Kamil Jod'z, 2018. "Mortality in a heterogeneous population - Lee-Carter's methodology," Papers 1803.11233, arXiv.org.
    4. Mohammed A. Bou-Rabee & Muhammad Yasin Naz & Imad ED. Albalaa & Shaharin Anwar Sulaiman, 2022. "BiLSTM Network-Based Approach for Solar Irradiance Forecasting in Continental Climate Zones," Energies, MDPI, vol. 15(6), pages 1-12, March.
    5. David Atance & Ana Debón & Eliseo Navarro, 2020. "A Comparison of Forecasting Mortality Models Using Resampling Methods," Mathematics, MDPI, vol. 8(9), pages 1-21, September.

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    More about this item

    Keywords

    GAS models; Mortality rates; Lee–Carter model; Forecasting; Observation-driven time series models;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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