Grouped multivariate and functional time series forecasting: An application to annuity pricing

Hanlin Shang*, Steven Haberman

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution


Age-specific mortality rates are often disaggregated by different attributes, such as sex, state, ethnic group and socioeconomic status. In making social policies and pricing annuities at national and sub-national levels, not only is it important to forecast mortality accurately, but also, forecasts at sub-national levels should add up to the forecasts at the national level. This motivates recent developments of grouped functional time series methods (Shang, Han and Rob Hyndman., 2017) to reconcile age-specific mortality forecasts. We extend these grouped functional time series forecasting methods to multivariate time series and apply them to produce point forecasts of mortality rates at older ages, from which fixed-term annuities for different ages and maturities can be priced. Using the regional age-specific mortality rates in Japan obtained from the Japanese
Mortality Database, we investigate the one-step-ahead to 15-step-ahead point forecast accuracy between the independent and grouped forecasting methods. The grouped forecasting methods are shown not only to be useful for reconciling forecasts of age-specific mortality rates at national and sub-national levels, but also to enjoy improved forecast accuracy. The improved forecast accuracy of mortality rates would be of great interest to the insurance and pension industries for estimating annuity prices, in particular at the level of population subgroups defined by key factors such as gender, region and socioeconomic grouping.
Original languageEnglish
Title of host publication2017 Living to 100 Monograph
PublisherSociety of Actuaries
Number of pages27
Publication statusPublished - 2017
Externally publishedYes
Event2017 Living to 100 Monograph - Orlando, United States
Duration: 4 Jan 20176 Jan 2017


Conference2017 Living to 100 Monograph
CountryUnited States

Bibliographical note

Also published as: Shang, H. L., & Haberman, S. (2017). Grouped multivariate and functional time series forecasting: An application to annuity pricing. Insurance: Mathematics and Economics, 75, 166-179. DOI: 10.1016/j.insmatheco.2017.05.007


  • forecast reconciliation
  • hierarchical time series
  • bottom-up method
  • optimal combination method
  • Lee-Carter method
  • Japanese Mortality Database


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