We study the modeling and forecasting of high-dimensional functional time series (HDFTS), which can be cross-sectionally correlated and temporally dependent. We introduce a decomposition of the HDFTS into two distinct components: a deterministic component and a residual component that varies over time. The decomposition is derived through the estimation of two-way functional analysis of variance. A functional time series forecasting method, based on functional principal component analysis, is implemented to produce forecasts for the residual component. By combining the forecasts of the residual component with the deterministic component, we obtain forecast curves for multiple populations. We apply the model to age- and sex-specific mortality rates in the United States, France, and Japan, in which there are 51 states, 95 departments, and 47 prefectures, respectively. The proposed method is capable of delivering more accurate point and interval forecasts in forecasting multi-population mortality than several benchmark methods considered.

翻译：我们研究了高维函数型时间序列（HDFTS）的建模与预测，该类序列同时具有截面相关性和时间依赖性。我们引入了一种HDFTS的分解方法，将其分为两个独立成分：确定性成分和随时间变化的残差成分。该分解通过双因素函数型方差分析的估计得出。基于函数型主成分分析的函数型时间序列预测方法被用于生成残差成分的预测。通过将残差成分的预测与确定性成分相结合，我们获得了多个总体的预测曲线。我们将该模型应用于美国、法国和日本的年龄与性别特异性死亡率数据，这三个国家分别包含51个州、95个省和47个县。与所考虑的几种基准方法相比，所提出的方法在预测多总体死亡率时能够提供更精确的点预测和区间预测。