We consider modeling and forecasting high-dimensional functional time series (HDFTS), which can be cross-sectionally correlated and temporally dependent. We present a novel two-way functional median polish decomposition, which is robust against outliers, to decompose HDFTS into deterministic and time-varying components. A functional time series forecasting method, based on dynamic functional principal component analysis, is implemented to produce forecasts for the time-varying components. By combining the forecasts of the time-varying components with the deterministic components, we obtain forecast curves for multiple populations. Illustrated by the age- and sex-specific mortality rates in the US, France, and Japan, which contain 51 states, 95 departments, and 47 prefectures, respectively, the proposed model delivers more accurate point and interval forecasts in forecasting multi-population mortality than several benchmark methods.

翻译：摘要：本文研究了可存在截面相关及时间依赖性的高维函数时间序列建模与预测问题。我们提出了一种基于双向函数中位数波兰分解的新方法，该方法对异常值具有稳健性，能够将高维函数时间序列分解为确定性成分与时变成分。通过实施基于动态函数主成分分析的函数时间序列预测方法，生成对时变成分的预测。将时变成分的预测结果与确定性成分相结合，可获得多个群体的预测曲线。以美国51个州、法国95个省及日本47个县（都道府县）的年龄与性别特异性死亡率为例，本模型在跨群体死亡率预测中的点预测与区间预测精度均优于多种基准方法。