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A parameterized approach to modeling and forecasting mortality

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  • Hatzopoulos, P.
  • Haberman, S.

Abstract

A new method is proposed of constructing mortality forecasts. This parameterized approach utilizes Generalized Linear Models (GLMs), based on heteroscedastic Poisson (non-additive) error structures, and using an orthonormal polynomial design matrix. Principal Component (PC) analysis is then applied to the cross-sectional fitted parameters. The produced model can be viewed either as a one-factor parameterized model where the time series are the fitted parameters, or as a principal component model, namely a log-bilinear hierarchical statistical association model of Goodman [Goodman, L.A., 1991. Measures, models, and graphical displays in the analysis of cross-classified data. J. Amer. Statist. Assoc. 86(416), 1085-1111] or equivalently as a generalized Lee-Carter model with p interaction terms. Mortality forecasts are obtained by applying dynamic linear regression models to the PCs. Two applications are presented: Sweden (1751-2006) and Greece (1957-2006).

Suggested Citation

  • Hatzopoulos, P. & Haberman, S., 2009. "A parameterized approach to modeling and forecasting mortality," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 103-123, February.
  • Handle: RePEc:eee:insuma:v:44:y:2009:i:1:p:103-123
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    References listed on IDEAS

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    2. Renshaw, A. E. & Haberman, S. & Hatzopoulos, P., 1997. "On the Duality of Assumptions Underpinning the Construction of Life Tables," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 27(01), pages 5-22, May.
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    5. Renshaw, A.E. & Haberman, S., 2008. "On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 797-816, April.
    6. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, April.
    7. Robert McNown & Andrei Rogers, 1989. "Forecasting Mortality: A Parameterized Time Series Approach," Demography, Springer;Population Association of America (PAA), vol. 26(4), pages 645-660, November.
    8. Heather Booth & Rob Hyndman & Leonie Tickle & Piet de Jong, 2006. "Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 15(9), pages 289-310, October.
    9. 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.
    10. Pitacco, Ermanno, 2004. "Survival models in a dynamic context: a survey," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 279-298, October.
    11. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
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    Cited by:

    1. George Mavridoglou & Peter Kiochos, 2011. "Sickness recovery intensities for short term health insurance in Greece," SPOUDAI Journal of Economics and Business, SPOUDAI Journal of Economics and Business, University of Piraeus, vol. 61(1-2), pages 39-54, january -.
    2. Ahmadi, Seyed Saeed & Li, Johnny Siu-Hang, 2014. "Coherent mortality forecasting with generalized linear models: A modified time-transformation approach," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 194-221.
    3. Hendrik Hansen, 2013. "The forecasting performance of mortality models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(1), pages 11-31, January.
    4. Valeria D’Amato & Steven Haberman & Gabriella Piscopo & Maria Russolillo, 2014. "Computational framework for longevity risk management," Computational Management Science, Springer, vol. 11(1), pages 111-137, January.
    5. repec:spr:demogr:v:54:y:2017:i:3:d:10.1007_s13524-017-0579-x is not listed on IDEAS
    6. David Blake & Andrew Cairns & Guy Coughlan & Kevin Dowd & Richard MacMinn, 2013. "The New Life Market," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 501-558, September.
    7. Hatzopoulos, P. & Haberman, S., 2015. "Modeling trends in cohort survival probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 162-179.
    8. repec:gam:jrisks:v:6:y:2018:i:2:p:44-:d:142754 is not listed on IDEAS
    9. Hatzopoulos, P. & Haberman, S., 2013. "Common mortality modeling and coherent forecasts. An empirical analysis of worldwide mortality data," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 320-337.

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