Coherent mortality forecasting by the weighted multilevel functional principal component approach

ABSTRACT

In 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.

Keywords:

• Human mortality
• coherent forecasts
• functional principal component analysis
• Lee-Carter model
• Product-Ratio model

Acknowledgements

The authors thank the Associate Editor and the reviewers for their constructive suggestions and very helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Bo Wang  http://orcid.org/0000-0001-6779-1933

Additional information

Funding

This work is based on part of the PhD thesis entitled ‘Gaussian Process and Functional Data Methods for Mortality Modelling’ by the first author from The University of Leicester. The work was supported by The Institute and Faculty of Actuaries (IFoA) and the College of Science and Engineering of the University of Leicester (UoL).