Dynamic principal component regression for forecasting functional time series in a group structure

When generating social policies and pricing annuity at national and subnational levels, it is essential both to forecast mortality accurately and ensure that forecasts at the subnational level add up to the forecasts at the national level. This has motivated recent developments in forecasting functional time series in a group structure, where static principal component analysis is used. In the presence of moderate to strong temporal dependence, static principal component analysis designed for independent and identically distributed functional data may be inadequate. Thus, through using the dynamic functional principal component analysis, we consider a functional time series forecasting method with static and dynamic principal component regression to forecast each series in a group structure. Through using the regional age-specific mortality rates in Japan obtained from the Japanese Mortality Database [(2019). National Institute of Population and Social Security Research. Available at http://www.ipss.go.jp/p-toukei/JMD/index-en.asp (data downloaded on 14 August 2018)], we investigate the point and interval forecast accuracies of our proposed extension, and subsequently make recommendations.