Abstract
ABSTRACTIn human mortality modelling, if a population consists of several subpopulations it can be desirable to model their mortality rates simultaneously while taking into account the heterogeneity among them. The mortality forecasting methods tend to result in divergent forecasts for subpopulations when independence is assumed. However, under closely related social, economic and biological backgrounds, mortality patterns of these subpopulations are expected to be non-divergent in the future. In this article, we propose a new method for coherent modelling and forecasting of mortality rates for multiple subpopulations, in the sense of nondivergent life expectancy among subpopulations. The mortality rates of subpopulations are treated as multilevel functional data and a weighted multilevel functional principal component (wMFPCA) approach is proposed to model and forecast them. The proposed model is applied to sex-specific data for nine developed countries, and the results show that, in terms of overall forecasting accuracy, the model outperforms the independent model and the Product-Ratio model as well as the unweighted multilevel functional principal component approach.
Highlights
As governments, insurance companies and pension funds are obliged to pay billions of pensions and annuities, they are heavily exposed to longevity risk due to the increasing life expectancy of pensioners and policy holders
We propose a new method, namely weighted multilevel functional principal component analysis, for coherent mortality forecasting, in the sense that the life expectancy in different populations does not diverge in the long run
We have proposed a new model for coherent forecasting of mortality rates for several correlated subpopulations in a large population
Summary
Insurance companies and pension funds are obliged to pay billions of pensions and annuities, they are heavily exposed to longevity risk due to the increasing life expectancy of pensioners and policy holders. Hyndman and Ullah [17] further extends the methods to a functional data framework which incorporates nonparametric smoothing, functional principal component decomposition and times series analysis into their model All of these works deal with forecasting mortality for a single population. Hyndman et al [14] develops the product-ratio method which achieves coherent mortality forecasting by the convergence of the ratios of the forecast age-specific death rates from any two subpopulations to appropriate constants Their numerical examples for Swedish sex-specific mortality data and Australian state-specific mortality data show that the forecasting accuracy is homogenised across subpopulations while the life expectancy in the long run presents convergence. We propose a new method, namely weighted multilevel functional principal component analysis (wMFPCA), for coherent mortality forecasting, in the sense that the life expectancy in different populations does not diverge in the long run.
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