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

Han Lin Shang, Rob J. Hyndman

Research output: Contribution to journalArticleResearchpeer-review

30 Citations (Scopus)


Age-specific mortality rates are often disaggregated by different attributes, such as sex, state, and ethnicity. Forecasting age-specific mortality rates at the national and sub-national levels plays an important role in developing social policy. However, independent forecasts at the sub-national levels may not add up to the forecasts at the national level. To address this issue, we consider reconciling forecasts of age-specific mortality rates, extending the methods of Hyndman et al. in 2011 to functional time series, 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 disaggregation factors. For evaluating forecast uncertainty, we propose a bootstrap method for reconciling interval forecasts. Using the regional age-specific mortality rates in Japan, obtained from the Japanese Mortality Database, we investigate the one- to ten-step-ahead point and interval forecast accuracies between the independent and grouped functional time series forecasting methods. The proposed methods are shown to be useful for reconciling forecasts of age-specific mortality rates at the national and sub-national levels. They also enjoy improved forecast accuracy averaged over different disaggregation factors. Supplementary materials for the article are available online.

Original languageEnglish
Pages (from-to)330-343
Number of pages14
JournalJournal of Computational and Graphical Statistics
Issue number2
Publication statusPublished - 3 Apr 2017


  • Bottom-up
  • Forecast reconciliation
  • Hierarchical time series forecasting
  • Japanese mortality database
  • Optimal combination

Cite this