We propose a nonstationary functional time series forecasting method with an application to age-specific mortality rates observed over the years. The method begins by taking the first-order differencing and estimates its long-run covariance function. Through eigen-decomposition, we obtain a set of estimated functional principal components and their associated scores for the differenced series. These components allow us to reconstruct the original functional data and compute the residuals. To model the temporal patterns in the residuals, we again perform dynamic functional principal component analysis and extract its estimated principal components and the associated scores for the residuals. As a byproduct, we introduce a geometrically decaying weighted approach to assign higher weights to the most recent data than those from the distant past. Using the Swedish age-specific mortality rates from 1751 to 2022, we demonstrate that the weighted dynamic functional factor model can produce more accurate point and interval forecasts, particularly for male series exhibiting higher volatility.

翻译：本文提出一种非平稳函数时间序列预测方法，并将其应用于多年观测的年龄别死亡率数据。该方法首先进行一阶差分处理，并估计其长期协方差函数。通过特征分解，我们获得差分序列的一组估计函数主成分及其对应得分。这些成分可用于重构原始函数数据并计算残差。为建模残差中的时序模式，我们再次执行动态函数主成分分析，提取残差的估计主成分及对应得分。作为衍生方法，我们引入几何衰减加权策略，为近期数据分配比远期数据更高的权重。基于瑞典1751年至2022年的年龄别死亡率数据，我们证明加权动态函数因子模型能够产生更精确的点预测与区间预测，尤其对波动性更高的男性序列效果显著。