Grouped functional time series forecasting: An application to age-specific mortality rates Seminar

Age-specific mortality rates are often disaggregated by different attributes, such as sex, state and ethnic group. Forecasting age-specific mortality rates at national and sub-national levels plays an important role in making societal policies associated with national and sub-national levels. Independent forecasts at sub-national levels may not add up to the forecasts at national level. To address this issue, we consider the problem of reconciling age-specific mortality rate forecasts from the viewpoint of grouped time series forecasting methods (Hyndman et al., 2011, Computational Statistics and Data Analysis), and extend these methods to functional time series forecasting, where age is considered as a continuum. The grouped functional time series methods are used to produce point forecasts of mortality rates that are aggregated appropriately across different levels of a hierarchy. To address forecast uncertainty, we also consider the reconciliation of interval forecasts through a maximum entropy bootstrap method which preserves the autocorrelation exhibited in the original functional time series. Using the regional age-specific mortality rates in Japan obtained from the Japanese Mortality Database, we investigate the one-step-ahead to 20-step-ahead point and interval forecast accuracies between the grouped functional time series and independent functional time series forecasting methods. The proposed methods are not only shown to be useful for reconciling forecasts of age-specific mortality rates at national and sub-national levels, but they also enjoy improved forecast accuracy. The improved forecast accuracy of mortality rates would be beneficial for government policy decision regarding the allocation of current and future resources, and would be of great interest to the insurance and pension industries.