The Annals of Applied Statistics

Mortality and life expectancy forecasting for a group of populations in developed countries: A multilevel functional data method

Han Lin Shang

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A multilevel functional data method is adapted for forecasting age-specific mortality for two or more populations in developed countries with high-quality vital registration systems. It uses multilevel functional principal component analysis of aggregate and population-specific data to extract the common trend and population-specific residual trend among populations. If the forecasts of population-specific residual trends do not show a long-term trend, then convergence in forecasts may be achieved. This method is first applied to age- and sex-specific data for the United Kingdom, and its forecast accuracy is then further compared with several existing methods, including independent functional data and product-ratio methods, through a multi-country comparison. The proposed method is also demonstrated by age-, sex- and state-specific data in Australia, where the convergence in forecasts can possibly be achieved by sex and state. For forecasting age-specific mortality, the multilevel functional data method is more accurate than the other coherent methods considered. For forecasting female life expectancy at birth, the multilevel functional data method is outperformed by the Bayesian method of Raftery, Lalic and Gerland [Demogr. Res. 30 (2014) 795–822]. For forecasting male life expectancy at birth, the multilevel functional data method performs better than the Bayesian methods in terms of point forecasts, but less well in terms of interval forecasts. Supplementary materials for this article are available online.

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Ann. Appl. Stat., Volume 10, Number 3 (2016), 1639-1672.

Received: March 2015
Revised: April 2016
First available in Project Euclid: 28 September 2016

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Augmented common factor method coherent forecasts functional time series life expectancy forecasting mortality forecasting product-ratio method


Shang, Han Lin. Mortality and life expectancy forecasting for a group of populations in developed countries: A multilevel functional data method. Ann. Appl. Stat. 10 (2016), no. 3, 1639--1672. doi:10.1214/16-AOAS953.

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Supplemental materials

  • Supplement to: “Mortality and life expectancy forecasting for a group of populations in developed countries: A multilevel functional data method.” by H. L. Shang. This supplement contains a PDF divided into four sections. Supplement A: Some theoretical properties of multilevel functional principal component decomposition; Supplement B: Derivation of posterior density of principal component scores and other variance parameters; Supplement C: WinBUGS computational code used for sampling principal component scores and estimating variance parameters from full conditional densities; Supplement D: Additional results for point and interval forecast accuracy of mortality and life expectancy, based on maximum forecast error measures.