  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 \cite{RLG14}.
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.
