Forecasting High-Dimensional Functional Time Series: Application to Sub-National Age-Specific Mortality
研究高维函数时间序列的建模与预测方法，通过分解为确定性和残差成分并分别预测，应用于美国、法国和日本次国家级年龄别死亡率数据，相比基准方法提高了点预测和区间预测的准确性。
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.