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


  • Han Lin Shang


  • Rob J Hyndman



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 of age-specific mortality rates at the sub-national levels may not add up to the forecasts at the national level. To address this issue, we consider the problem of reconciling age-specific mortality rate forecasts from the viewpoint of grouped univariate time series forecasting methods (Hyndman, Ahmed, et al., 2011), 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 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, and they also enjoy improved forecast accuracy averaged over different disaggregation factors.

Suggested Citation

  • Han Lin Shang & Rob J Hyndman, 2016. "Grouped functional time series forecasting: An application to age-specific mortality rates," Monash Econometrics and Business Statistics Working Papers 4/16, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2016-4

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    References listed on IDEAS

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    8. Lei Fang & Wolfgang K. Härdle, 2015. "Stochastic Population Analysis: A Functional Data Approach," SFB 649 Discussion Papers SFB649DP2015-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    Cited by:

    1. Han Lin Shang, 2017. "Reconciling Forecasts of Infant Mortality Rates at National and Sub-National Levels: Grouped Time-Series Methods," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 36(1), pages 55-84, February.
    2. repec:gam:jrisks:v:5:y:2017:i:3:p:42-:d:106077 is not listed on IDEAS
    3. Daniel Kosiorowski & Dominik Mielczarek & Jerzy P. Rydlewski, 2017. "Aggregated moving functional median in robust prediction of hierarchical functional time series - an application to forecasting web portal users behaviors," Papers 1710.02669,, revised Jul 2018.

    More about this item


    Forecast reconciliation; hierarchical time series forecasting; bottom-up; optimal combination; Japanese Mortality Database;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts

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