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

TL;DR

This paper develops grouped functional time series methods to improve the accuracy of forecasting age-specific mortality rates across different regions and attributes, ensuring consistency between national and sub-national forecasts.

Contribution

It extends existing functional time series forecasting techniques to incorporate grouping and reconciliation, enhancing forecast accuracy and consistency across disaggregation levels.

Findings

Grouped methods outperform independent forecasts in accuracy.

Bootstrap-based interval forecasts effectively quantify uncertainty.

Reconciled forecasts are consistent across national and regional levels.

Abstract

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. (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. Supplemental materials for the article are available online.