×

Evaluating the goodness of fit of stochastic mortality models. (English) Zbl 1231.91179

Summary: This study sets out a framework to evaluate the goodness of fit of stochastic mortality models and applies it to six different models estimated using English & Welsh male mortality data over ages 64–89 and years 1961–2007. The methodology exploits the structure of each model to obtain various residual series that are predicted to be iid standard normal under the null hypothesis of model adequacy. Goodness of fit can then be assessed using conventional tests of the predictions of iid standard normality. The models considered are: Lee and Carter’s (1992) one-factor model, a version of Renshaw and Haberman’s (2006) extension of the Lee-Carter model to allow for a cohort-effect, the age-period-cohort model, which is a simplified version of the Renshaw-Haberman model, the 2006 Cairns-Blake-Dowd two-factor model and two generalized versions of the latter that allow for a cohort-effect. For the data set considered, there are some notable differences amongst the different models, but none of the models performs well in all tests and no model clearly dominates the others.

MSC:

91B30 Risk theory, insurance (MSC2010)
91B70 Stochastic models in economics
62P05 Applications of statistics to actuarial sciences and financial mathematics

Software:

LifeMetrics; Dowd
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Booth, H.; Maindonald, J.; Smith, L., Applying lee – carter under conditions of variable mortality decline, Population studies, 56, 325-336, (2002)
[2] Booth, H., Maindonald, J., Smith, L., 2002b. Age-time interactions in mortality projection: aplying Lee-Carter to Australia, Working Papers in Demography, The Australian National University.
[3] Booth, H.; Hyndman, R.J.; Tickle, L.; De Jong, P., Lee – carter mortality forecasting: a multi-country comparison of variants and extensions, Demographic research, 15, 289-310, (2006)
[4] Brouhns, N.; Denuit, M.; Vermunt, J.K., A Poisson log-bilinear regression approach to the construction of projected lifetables, Insurance: mathematics and economics, 31, 373-393, (2002) · Zbl 1074.62524
[5] 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)
[6] Cairns, A.J.G.; Blake, D.; Dowd, K., Pricing death: frameworks for the valuation and securitization of mortality risk, ASTIN bulletin, 36, 79-120, (2006) · Zbl 1162.91403
[7] 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 & wales and the united states, North American actuarial journal, 13, 1-35, (2009)
[8] Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Khalaf-Allah, M., 2010. A framework for forecasting mortality rates with an application to six stochastic mortality models. Pensions Institute Discussion Paper PI-0801, March. · Zbl 1231.91179
[9] Cochrane, J.H., How big is the random walk in GNP?, Journal of political economy, 96, 893-920, (1988)
[10] CMI,, 2006. Stochastic projection methodologies: Further progress and P-Spline model features, example results and implications. Working Paper 20, Continuous Mortality Investigation. Available at: http://www.actuaries.org.uk/knowledge/cmi/cmi_wp/wp20.
[11] CMI,, 2007. Stochastic projection methodologies: Lee-Carter model features, example results and implications. Working Paper 25, Continuous Mortality Investigation. Available at: http://www.actuaries.org.uk/knowledge/cmi/cmi_wp/wp25.
[12] Coughlan, G.D., Epstein, D., Ong, A., Sinha, A., Balevich, I., Hevia Portocarrera, J., Gingrich, E., Khalaf-Allah, M., Joseph, P., 2007. LifeMetrics: A toolkit for measuring and managing longevity and mortality risks. Technical Document (JPMorgan, London, 13 March). Available at: www.lifemetrics.com.
[13] Currie, I.D.; Durban, M.; Eilers, P.H.C., Smoothing and forecasting mortality rates, Statistical modelling, 4, 279-298, (2004) · Zbl 1061.62171
[14] Currie, I.D., 2006. Smoothing and forecasting mortality rates with P-splines. Presentation to the Institute of Actuaries. www.ma.hw.ac.uk/ iain/research.talks.html.
[15] Dowd, K., Measuring market risk, (2005), John Wiley Chichester and New York
[16] Dowd, K., Cairns, A.J.G., Blake, D., Coughlan, G.D., Epstein, D., Khalaf- Allah, M., 2010. Backtesting stochastic mortality models: An ex-post evaluation of multi-period-ahead density forecasts. North American Actuarial Journal, forthcoming. · Zbl 1231.91179
[17] Jacobsen, R.; Keiding, N.; Lynge, E., Long-term mortality trends behind low life expectancy of danish women, J. epidemiol. community health, 56, 205-208, (2002)
[18] Jarque, C.; Bera, A., Efficient tests for normality, homoscedasticity and serial independence of regression residuals, Economics letters, 6, 255-259, (1980)
[19] Hanewald, K., 2009. Mortality modeling: Lee-Carter and the macroeconomy. Discussion Paper, Humboldt-Universität zu Berlin, May 19, 2009, available at SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1336888.
[20] Huang, H.-C.; Yue, J.C.; Yang, S.S., An empirical study of mortality models in Taiwan, Asia-Pacific journal of risk and insurance, 3, 140-154, (2008)
[21] Hyndman, R.J.; Ullah, M.S., Robust forecasting of mortality and fertility rates: a functional data approach, Computational statistics & data analysis, 51, 4942-4956, (2007) · Zbl 1162.62434
[22] Lee, R.D.; Carter, L.R., Modeling and forecasting US mortality, Journal of the American statistical association, 87, 659-675, (1992) · Zbl 1351.62186
[23] Li, J.S-H.; Hardy, M.R.; Tan, K.S., Uncertainty in mortality forecasting: an extension to the classic lee – carter approach, ASTIN bulletin, 39, 137-164, (2009) · Zbl 1203.91113
[24] Lo, A.W.; MacKinley, A.C., Stock prices do not follow random walks: evidence based on a simple specification test, Review of financial studies, 1, 41-66, (1988)
[25] Lo, A.W.; MacKinley, A.C., The size and power of the variance ratio test in finite samples: a Monte Carlo investigation, Journal of econometrics, 40, 203-238, (1989)
[26] Osmond, C., Using age, period and cohort models to estimate future mortality rates, International journal of epidemiology, 14, 124-129, (1985)
[27] 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
[28] Sweeting, P., 2009. A Trend-Change Extension of the Cairns-Blake-Dowd Model, Pensions Institute Discussion Paper PI-0904, February.
[29] Wilmoth, J.R., Is the pace of Japanese mortality decline converging toward international trends?, Population and development review, 24, 593-600, (1998)
[30] Yang, S.S.; Yue, J.C.; Huang, H.-C., Modeling longevity risks using a principal component approach: a comparison with existing stochastic mortality models, Insurance: mathematics and economics, 46, 254-270, (2010) · Zbl 1231.91254
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.