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A dynamic parameterization modeling for the age-period-cohort mortality. (English) Zbl 1218.91082

Summary: An extended version of the authors [Insur. Math. Econ. 44, No. 1, 103–123 (2009; Zbl 1156.91394)] dynamic parametric model is proposed for analyzing mortality structures, incorporating the cohort effect. A one-factor parameterized exponential polynomial in age effects within the generalized linear models (GLM) framework is used. Sparse principal component analysis (SPCA) is then applied to time-dependent GLM parameter estimates and provides (marginal) estimates for a two-factor principal component (PC) approach structure. Modeling the two-factor residuals in the same way, in age-cohort effects, provides estimates for the (conditional) three-factor age-period-cohort model. The age-time and cohort related components are extrapolated using dynamic linear regression (DLR) models. An application is presented for England & Wales males (1841–2006).

MSC:

91B30 Risk theory, insurance (MSC2010)
91D20 Mathematical geography and demography
62P05 Applications of statistics to actuarial sciences and financial mathematics

Citations:

Zbl 1156.91394

Software:

DSPCA
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[1] Bell, W.R., Monsell, B.C., 1991. Using principal components in time series modelling and forecasting of age-specific mortality rates. In: Proceedings of the American Statistical Association, Social Statistics Section, pp. 154-159.
[2] Booth, H.; Tickle, L., Mortality modelling and forecasting: a review of methods, Annals of actuarial science, 3, 1-2, 3-43, (2008)
[3] Brillinger, D.R., The natural variability of vital rates and associated statistics, Biometrics, 42, 2, 693-734, (1986) · Zbl 0611.62136
[4] Brouhns, N.; Denuit, M.; Vermunt, J.K., A Poisson log-bilinear approach to the construction of projected life tables, Insurance: mathematics & economics, 31, 3, 373-393, (2002) · Zbl 1074.62524
[5] Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Khalaf-Allah, M., 2008. Mortality density forecasts: an analysis of six stochastic mortality models. Pensions Institute Discussion Paper PI-0801. Pensions Institute, Cass Business School.
[6] 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, 1-35, (2009)
[7] Coale, A.J.; Kisker, E.E., Defects in data on old-age mortality in the united states: new procedures for calculating schedules and life tables at the highest ages, Asian and Pacific population forum, 4, 1, 1-31, (1990)
[8] Currie, I.D.; Durban, M.; Eilers, P.H.C., Smoothing and forecasting mortality rates, Statistical modelling, 4, 4, 279-298, (2004) · Zbl 1061.62171
[9] De Jong, P.; Tickle, L., Extending lee – carter mortality forecasting, Mathematical population studies, 13, 1, 1-18, (2006) · Zbl 1151.91742
[10] Gao, Q.; Hu, C., Dynamic factor model with conditional heteroskedasticity, Insurance: mathematics & economics, 45, 2, 410-423, (2009) · Zbl 1231.91187
[11] Harvey, A., Forecasting, structural time series models and the Kalman filter, (1991), Cambridge University Press
[12] Hatzopoulos, P.; Haberman, S., A parameterized approach to modelling and forecasting mortality, Insurance: mathematics and economics, 44, 1, 103-123, (2009) · Zbl 1156.91394
[13] Heligman, L.; Pollard, J.H., The age pattern of mortality, Journal of the institute of actuaries, 107, 49-80, (1980)
[14] Horiuchi, S.; Wilmoth, J.R., Deceleration in the age pattern of mortality at older ages, Demography, 35, 4, 391-412, (1998)
[15] Hyndman, R.J., Ullah, M.S., 2005. Robust forecasting of mortality and fertility rates: a functional data approach. Working Paper. Department of Economics and Business Statistics, Monash University. http://www.robhyndman.info/papers/funcfor.htm. · Zbl 1162.62434
[16] Lansangan, J.R.; Barrios, E.B., Principal components analysis of nonstationary time series data, Statistics and computing, 19, 2, 173-187, (2009)
[17] Lazar, D.; Denuit, M., A multivariate time series approach to projected life tables, Applied stochastic models in business & industry, 25, 6, 806-823, (2009) · Zbl 1224.91069
[18] Ledermann, S.; Breas, J., LES dimensions de la mortalite, Population, 14, 637-682, (1959)
[19] Lee, R.D.; Carter, L.R., Modelling and forecasting US mortality, Journal of the American statistical association, 87, 659-671, (1992)
[20] Luss, R., Aspremont, A., 2006. DSPCA: a toolbox for sparse principal component analysis. Mathematical Subject Classification: 90C90, 62H25, 65K05.
[21] Mode, C.; Busby, R.C., An eight-parameter model of human mortality—the single decrement case, Bulletin of mathematical biology, 44, 5, 647-659, (1982) · Zbl 0494.62089
[22] Pitacco, E., Survival models in dynamic context: a survey, Insurance: mathematics & economics, 35, 2, 279-298, (2004) · Zbl 1079.91050
[23] Pitacco, E.; Denuit, M.; Haberman, S.; Olivieri, A., Modelling longevity dynamics for pensions and annuity business, (2009), Oxford University Press · Zbl 1163.91005
[24] Renshaw, A.E.; Haberman, S., Lee – carter mortality forecasting with age-specific enhancement, Insurance: mathematics and economics, 33, 2, 255-272, (2003) · Zbl 1103.91371
[25] Renshaw, A.E.; Haberman, S., Lee – carter mortality forecasting, a parallel generalized linear modelling approach for england & wales mortality projections, Applied statistics, 52, 1, 119-137, (2003) · Zbl 1111.62359
[26] Renshaw, A.E.; Haberman, S., On the forecasting of mortality reduction factors, Insurance: mathematics and economics, 32, 3, 379-401, (2003) · Zbl 1025.62041
[27] Renshaw, A.E.; Haberman, S., A cohort-based extension to the lee – carter model for mortality reduction factors, Insurance: mathematics and economics, 38, 3, 556-570, (2006) · Zbl 1168.91418
[28] Richards, S.J.J.; Kirkby, G.; Currie, I.D., The importance of year of birth in two-dimensional mortality data, British actuarial journal, 12, I, 5-61, (2005)
[29] Rogers, A.; Little, J.S., Parameterizing age patterns of demographic rates with the multiexponential model schedule, Mathematical population studies, 4, 3, 175-195, (1994) · Zbl 0877.92038
[30] Rogers, A., Planck, F., 1984. Parameterized multistage population projections. Working Paper for Presentation at the Annual Meeting of the Population Association of America. Minnesota, May 3-5.
[31] Siler, W., Parameters of mortality in human populations with widely varying life spans, Statistics in medicine, 2, 373-380, (1983)
[32] Sithole, T.Z.; Haberman, S.; Verrall, R.J., An investigation into parametric models for mortality projections, with applications to immediate annuitants and life office pensioners’ data, Insurance: mathematics and economics, 27, 3, 285-312, (2000) · Zbl 1055.62555
[33] Taylor, C.J., 2007. Engineering Department. Lancaster University, Lancaster, LA1 4YR, United Kingdom. Web: http://www.es.lancs.ac.uk/cres/captain/.
[34] Willets, R.C., The cohort effect: insights and explanations, British actuarial journal, 10, 4, 833-877, (2004)
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