Modelling dependent data for longevity projections
The risk profile of an insurance company involved in annuity business is heavily affected by the uncertainty in future mortality trends. It is problematic to capture accurately future survival patterns, in particular at retirement ages when the effects of the rectangularization phenomenon and random fluctuations are combined. Another important aspect affecting the projections is related to the so-called cohort-period effect. In particular, the mortality experience of countries in the industrialized world over the course of the twentieth century would suggest a substantial age–time interaction, with the two dominant trends affecting different age groups at different times. From a statistical point of view, this indicates a dependence structure. Also the dependence between ages is an important component in the modeling of mortality (Barrieu et al., 2011). It is observed that the mortality improvements are similar for individuals of contiguous ages (Wills and Sherris, 2008). Moreover, considering the data subdivided by set by single years of age, the correlations between the residuals for adjacent age groups tend to be high (as noted in Denton et al., 2005). This suggests that there is value in exploring the dependence structure, also across time, in other words the inter-period correlation. The aim of this paper is to improve the methodology for forecasting mortality in order to enhance model performance and increase forecasting power by capturing the dependence structure of neighboring observations in the population. To do this, we adapt the methodology for measuring uncertainty in projections in the Lee–Carter context and introduce a tailor-made bootstrap instead of an ordinary bootstrap. The approach is illustrated with an empirical example.
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- Arthur Renshaw & Steven Haberman, 2003. "Lee-Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 119-137.
- 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.
- Rob J. Hyndman & Md. Shahid Ullah, 2005.
"Robust forecasting of mortality and fertility rates: a functional data approach,"
Monash Econometrics and Business Statistics Working Papers
2/05, Monash University, Department of Econometrics and Business Statistics.
- 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.
- 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.
- Edwin Choi & Peter Hall, 2000. "Bootstrap confidence regions computed from autoregressions of arbitrary order," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 461-477.
- Koissi, Marie-Claire & Shapiro, Arnold F. & Hognas, Goran, 2006. "Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 1-20, February.
- Renshaw, A. E. & Haberman, S., 2003. "On the forecasting of mortality reduction factors," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 379-401, July.
- Frank Denton & Christine Feaver & Byron Spencer, 2005. "Time series analysis and stochastic forecasting: An econometric study of mortality and life expectancy," Journal of Population Economics, Springer, vol. 18(2), pages 203-227, 06.
- Pauline Barrieu & Harry Bensusan & Nicole El Karoui & Caroline Hillairet & Stéphane Loisel & Claudia Ravanelli & Yahia Salhi, 2012. "Understanding, Modeling and Managing Longevity Risk: Key Issues and Main Challenges," Post-Print hal-00417800, HAL.
- Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272, July.
- Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, 07.
- 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.
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