Sieve bootstrapping in the Lee-Carter model
This paper studies an alternative approach to construct confidence intervals for parameter estimates of the Lee-Carter model. First, the procedure of obtaining confidence intervals using regular nonparametric i.i.d. bootstrap is specified. Empirical evidence seems to invalidate this approach as it indicates strong autocorrelation and cross correlation in the residuals. A more general approach is introduced, relying on the Sieve bootstrap method, that includes the nonparametric i.i.d. method as a special case. Secondly, this paper examines the performance of the nonparametric i.i.d. and the Sieve bootstrap approach. In an application to a Dutch data set, the Sieve bootstrap method returns much wider confidence intervals compared to the nonparametric i.i.d. approach. Neglecting the residuals dependency structure, the nonparametric i.i.d. bootstrap method seems to construct confidence intervals that are too narrow. Third, the paper discusses an intuitive explanation for the source of autocorrelation and cross correlation within stochastic mortality models.
|Date of creation:||2013|
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- 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.
- 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.
- 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.
- 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.
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