We study the modeling and forecasting of high-dimensional functional time series, which can be temporally dependent and cross-sectionally correlated. We implement a functional analysis of variance (FANOVA) to decompose high-dimensional functional time series, such as subnational age- and sex-specific mortality observed over years, into two distinct components: a deterministic mean structure and a residual process varying over time. Unlike purely statistical dimensionality-reduction techniques, the FANOVA decomposition provides a direct and interpretable framework by partitioning the series into effects attributable to data-specific factors, such as regional and sex-level variations, and a grand functional mean. From the residual process, we implement a functional factor model to capture the remaining stochastic trends. By combining the forecasts of the residual component with the estimated deterministic structure, we obtain the forecasted curves for high-dimensional functional time series. Illustrated by the age-specific Japanese subnational mortality rates from 1975 to 2023, we evaluate and compare the accuracy of the point and interval forecasts across various forecast horizons. The results demonstrate that leveraging these interpretable components not only clarifies the underlying drivers of the data but also improves forecast accuracy, providing more transparent insights for evidence-based policy decisions.

翻译：我们研究了高维函数时间序列的建模与预测问题，该类数据同时存在时间依赖性和横截面相关性。通过实施函数方差分析（FANOVA），我们将高维函数时间序列（例如按年份观测的国家以下层面年龄-性别特异性死亡率）分解为两个不同组成部分：确定性均值结构和随时间变化的残差过程。与纯统计降维技术不同，FANOVA分解通过将序列划分为可归因于数据特定因素（如地区与性别差异）的效应及整体函数均值，提供了直接且可解释的框架。基于残差过程，我们采用函数因子模型捕捉剩余的随机趋势。通过将残差成分的预测与估计的确定性结构相结合，即可获得高维函数时间序列的预测曲线。以1975年至2023年日本地区年龄特异性死亡率数据为例，我们评估并比较了不同预测区间内的点预测与区间预测精度。结果表明，利用这些可解释成分不仅能阐明数据背后的潜在驱动因素，还可提高预测精度，为循证政策制定提供更透明的见解。