Finding an optimal sample size for the Lee-Carter model: A Bayesian approach

  • Hong Li Hong Li

In this thesis, we aim to nd an age-specific sample size for the Lee-Carter model that maximizes the likelihood in the out-of-sample forecast. We set up a dynamic sequential Bayesian updating model which explicitly models the sample size as one of its parameters. Markov Chain Monte Carlo methods are used to fit the model and to sample from the posterior predictive distributions. This model is applied to the sex neutral mortality rates of the Dutch populationfrom 1928 to 2009 for ages from 0 to 99, and results for age 0, 25, 50, 75, and 90 are reported. We present a dynamic algorithm as well as a reduced static application. Results from the static model show that the means of the conditional posterior densities of sample size for the 5 ages range from 31 to 34, while in their dynamic counterpart, they turn out to be 33.7 and 32.6 for age 0 and 25, respectively, and from 38 to 43 for the other three ages. In addition,the standard deviations of the conditional posterior density of the sample size obtained from the static model are approximately 11 for all ages. In the dynamic case, nevertheless, the standard deviations range from 3 to 5. Furthermore, the dynamic model delivers narrower con dence intervals than the ones obtained from the static model, but, except for age 0, still mildly wider than the originalLee-Carter model.

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