×

Stochastic life table forecasting: a time-simultaneous fan chart application. (English) Zbl 1499.62385

Summary: 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.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Akaike, H., A new look at the statistical model identification, IEEE Transactions on Automatic Control, AC-19, 716-723 (1974) · Zbl 0314.62039
[2] Blake, D.; Cairns, A. J.G.; Dowd, K., Longevity risk and the Grim Reaper’s toxic tail: the survivor fan charts, Insurance: Mathematics and Economics, 42, 1062-1066 (2008) · Zbl 1141.91485
[3] Cairns, A. J.G.; Blake, D.; Dowd, K., A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration, Journal of Risk and Insurance, 73, 687-718 (2006)
[4] Cairns, A. J.G.; Blake, D.; Dowd, K.; Coughlan, G. D.; Epstein, D.; Ong, A.; Balevich, I., A quantitative comparison of stochastic mortality models using data from England and Wales and the United States, North American Actuarial Journal, 13, 1-35 (2009) · Zbl 1484.91376
[5] Continuous Mortality Investigation Bureau, Standard tables of mortality based on the 1991-94 experiences, CMI Report no. 17, London: Institute of Actuaries and Faculty of Actuaries, 1999.; Continuous Mortality Investigation Bureau, Standard tables of mortality based on the 1991-94 experiences, CMI Report no. 17, London: Institute of Actuaries and Faculty of Actuaries, 1999.
[6] Continuous Mortality Investigation Bureau, An interim basis for adjusting the “92” series mortality projections for cohort effects, CMI Working Paper 1, London: Institute of Actuaries and Faculty of Actuaries, 2002.; Continuous Mortality Investigation Bureau, An interim basis for adjusting the “92” series mortality projections for cohort effects, CMI Working Paper 1, London: Institute of Actuaries and Faculty of Actuaries, 2002.
[7] Continuous Mortality Investigation Bureau, Projecting future mortality: a discussion paper, CMI Working Paper no. 3, London: Institute of Actuaries and Faculty of Actuaries, 2004.; Continuous Mortality Investigation Bureau, Projecting future mortality: a discussion paper, CMI Working Paper no. 3, London: Institute of Actuaries and Faculty of Actuaries, 2004.
[8] Delwarde, A.; Denuit, M.; Partrat, C., Negative binomial version of the Lee-Carter model for mortality forecasting, Applied Stochastic Models in Business and Industry, 23, 385-401 (2007) · Zbl 1150.91426
[9] Dowd, K.; Blake, D.; Cairns, A. J.G., Facing up to uncertain life expectancy: the longevity fan charts, Demography, 47, 67-78 (2010)
[10] Dowd, K.; Cairns, A. J.G.; Blake, D.; Coughlan, G. D.; Epstein, D.; Khalaf-Allah, M., Evaluating the goodness of fit of stochastic mortality models, Insurance: Mathematics and Economics, 47, 255-265 (2010) · Zbl 1231.91179
[11] Dowd, K.; Cairns, A. J.G.; Blake, D.; Coughlan, G. D.; Epstein, D.; Khalaf-Allah, M., Backtesting stochastic mortality models: an ex-post evaluation of multi-period-ahead density forecasts, North American Actuarial Journal, 14, 281-298 (2010)
[12] Human Mortality Database, University of California, Berkeley (USA), and Max Planck Institute of Demographic Research (Germany), 2011 (http://www.mortality.orghttp://www.humanmortality.de; Human Mortality Database, University of California, Berkeley (USA), and Max Planck Institute of Demographic Research (Germany), 2011 (http://www.mortality.orghttp://www.humanmortality.de
[13] Kolsrud, D., Time-simultaneous prediction band for a time series, Journal of Forecasting, 26, 171-188 (2007)
[14] Lee, R.; Carter, L., Modeling and forecasting U.S. mortality, Journal of the American Statistical Association, 87, 659-671 (1992) · Zbl 1351.62186
[15] Li, J. S.H.; Hardy, M. R.; Tan, K. S., Uncertainty in mortality forecasting: an extension to the classical Lee-Carter approach, ASTIN Bulletin, 39, 137-164 (2009) · Zbl 1203.91113
[16] Nair, V. N., Confidence bands for survival functions with censored data: a comparative study, Technometrics, 26, 265-275 (1984)
[17] Parigi, G.; Schlitzer, G., Quarterly forecasts of the Italian business cycle by means of monthly economic indicators, Journal of Forecasting, 14, 117-141 (1995)
[18] Renshaw, A. E.; Haberman, S., Lee-Carter mortality forecasting with age-specific enhancement, Insurance: Mathematics and Economics, 33, 255-272 (2003) · Zbl 1103.91371
[19] Renshaw, A. E.; Haberman, S., A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insurance: Mathematics and Economics, 38, 556-570 (2006) · Zbl 1168.91418
[20] Scheike, T. H.; Zhang, M-. J., Extensions and applications of the Cox-Aalen survival model, Biometrics, 59, 1036-1045 (2003) · Zbl 1274.62678
[21] Schwarz, G., Estimating the dimension of a Model, Annals of Statistics, 6, 461-464 (1978) · Zbl 0379.62005
[22] Tuljapurkar, S., Future mortality: a bumpy road to Shangri-La?, Science of Aging Knowledge Environment, 14, 9 (2005)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.