Abstract
In this paper, we quantitatively compare the forecasts from four different mortality models. We consider one discrete-time model proposed by Lee and Carter (1992) and three continuous-time models: the Wills and Sherris (2011) model, the Feller process and the Ornstein-Uhlenbeck (OU) process. The first two models estimate the whole surface of mortality simultaneously, while in the latter two, each generation is modelled and calibrated separately. We calibrate the models to UK and Australian population data. We find that all the models show relatively similar absolute total error for a given dataset, except the Lee-Carter model, whose performance differs significantly. To evaluate the forecasting performance we therefore look at two alternative measures: the relative error between the forecasted and the actual mortality rates and the percentage of actual mortality rates which fall within a prediction interval. In terms of the prediction intervals, the results are more divergent since each model implies a different structure for the variance of mortality rates. According to our experiments, the Wills and Sherris model produces superior results in terms of the prediction intervals. However, in terms of the mean absolute error, the OU and the Feller processes perform better. The forecasting performance of the Lee Carter model is mostly dependent on the choice of the dataset.
Highlights
One of the main issues facing financial and governmental institutions, within the current economic climate, is the forecasting of mortality among an elderly population
It has been shown that the Lee-Carter model is a special type of multivariate random walk with a drift (RWD), in which the covariance matrix depends on the drift vector
To have reliable estimation results and to make the comparison between the models which simulate the whole mortality surface and the ones which model each generation separately fairer, we take all possible generations from the data, which satisfy the criteria that the length of the backtesting period would not be less than 10 years
Summary
One of the main issues facing financial and governmental institutions, within the current economic climate, is the forecasting of mortality among an elderly population. The future projections for survival probabilities are made, their closeness to the historical values is discussed, but not evaluated quantitatively Another continuous-time mortality model we consider in this work is the one proposed by Wills and Sherris (2011) [13] for the Australian population. Dowd et al [16] formally evaluate the forecasting performance of six different stochastic mortality models applied to male mortality data for England and Wales. They use a backtesting procedure to test the stability of forecasts over different time horizons and conclude that the investigated models perform adequately, and that there is little difference between them.
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