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Stochastic life table forecasting: A time-simultaneous fan chart application

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  • Li, J.S.H.
  • Ng, A.C.Y.
  • Chan, W.S.

Abstract

Given a fitted stochastic mortality model, we can express the uncertainty associated with future death rates in terms of confidence or prediction intervals. Recently, a group of researchers have proposed using fan charts to display prediction intervals for future mortality rates. Existing mortality fan charts are based on isolated pointwise prediction intervals. By pointwise we mean that the interval reflects uncertainty in a quantity at a single point of time, but it does not account for any dynamic property of the time-series. In this paper, we overcome this limitation by introducing the concept of time-simultaneous fan charts. In more detail, instead of pointwise intervals, a time-simultaneous fan chart is derived from a prediction band with a prescribed probability of covering the whole time trajectory. We present two numerical methods for producing time-simultaneous fan charts. These methods can be applied to common stochastic mortality models, including the generalized Cairns–Blake–Dowd model. Finally, the proposed method is illustrated with mortality data from the populations of Australia and New Zealand.

Suggested Citation

  • Li, J.S.H. & Ng, A.C.Y. & Chan, W.S., 2013. "Stochastic life table forecasting: A time-simultaneous fan chart application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 93(C), pages 98-107.
    • Handle: RePEc:eee:matcom:v:93:y:2013:i:c:p:98-107
    DOI: 10.1016/j.matcom.2012.08.007
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    References listed on IDEAS

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    1. Andrew Cairns & David Blake & Kevin Dowd & Guy Coughlan & David Epstein & Alen Ong & Igor Balevich, 2009. "A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(1), pages 1-35.
    2. Renshaw, A.E. & Haberman, S., 2006. "A cohort-based extension to the Lee-Carter model for mortality reduction factors," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 556-570, June.
    3. 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.
    4. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718, December.
    5. Blake, David & Dowd, Kevin & Cairns, Andrew J.G., 2008. "Longevity risk and the Grim Reaper's toxic tail: The survivor fan charts," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1062-1066, June.
    6. Kevin Dowd & Andrew Cairns & David Blake & Guy Coughlan & David Epstein & Marwa Khalaf-Allah, 2010. "Backtesting Stochastic Mortality Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(3), pages 281-298.
    7. Kevin Dowd & David Blake & Andrew Cairns, 2010. "Facing up to uncertain life expectancy: The longevity fan charts," Demography, Springer;Population Association of America (PAA), vol. 47(1), pages 67-78, February.
    8. Li, Johnny Siu-Hang & Hardy, Mary R. & Tan, Ken Seng, 2009. "Uncertainty in Mortality Forecasting: An Extension to the Classical Lee-Carter Approach," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 137-164, May.
    9. Dowd, Kevin & Cairns, Andrew J.G. & Blake, David & Coughlan, Guy D. & Epstein, David & Khalaf-Allah, Marwa, 2010. "Evaluating the goodness of fit of stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 255-265, December.
    10. 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.
    11. Dag Kolsrud, 2007. "Time-simultaneous prediction band for a time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(3), pages 171-188.
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    Cited by:

    1. Michael McAleer & Felix Chan & Les Oxley, 2013. "Modeling and Simulation: An Overview," Working Papers in Economics 13/18, University of Canterbury, Department of Economics and Finance.
    2. Kevin Dowd & David Blake & Andrew J. G. Cairns, 2016. "The Myth of Methuselah and the Uncertainty of Death: The Mortality Fan Charts," Risks, MDPI, vol. 4(3), pages 1-7, July.

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