ABSTRACT 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.

中文翻译：

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用于预测组结构中功能时间序列的动态主成分回归

摘要 在国家和国家以下层面制定社会政策和年金定价时，准确预测死亡率并确保国家以下层面的预测与国家层面的预测相加是必不可少的。这推动了在使用静态主成分分析的组结构中预测功能时间序列的最新发展。在存在中度至强时间依赖性的情况下，为独立和同分布的函数数据设计的静态主成分分析可能是不够的。因此，通过使用动态函数主成分分析，我们考虑使用静态和动态主成分回归的函数时间序列预测方法来预测组结构中的每个序列。通过使用从日本死亡率数据库中获得的日本区域年龄别死亡率 [(2019)。国家人口与社会保障研究所。可在 http://www.ipss.go.jp/p-toukei/JMD/index-en.asp（数据于 2018 年 8 月 14 日下载）]，我们调查了我们提议的扩展的点和区间预测精度，然后提出建议。