Interpretable models for forecasting high-dimensional functional time series
高维函数型时间序列预测的可解释模型AI 解读 ↓
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高维函数型时间序列预测的可解释模型
- 研究问题
- 面对同时具有时间依赖与横截面相关的高维曲线数据，如何保持地区、性别等结构的可解释性，并改善点预测和区间预测？
- 方法与思路
- 作者先以函数型方差分析分离确定性均值结构和时变残差，再对残差建立函数型因子模型，合并两部分得到预测曲线。
- 材料陈述的贡献
- 摘要称，在日本地区死亡率应用中，该分解增强解释性，且相较某一现有方法，点预测精度改善约百分之二十五至四十五。
- 阅读关注点
- 应核对均值分解约束、因子提取和预测方法、训练与评价窗口，以及精度改善采用的损失指标和区间预测覆盖表现。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收；摘要未说明比较基准细节，所述精度改善不能直接推广到其他数据。
原文摘要
We study the modeling and forecasting of high-dimensional functional time series, which can be temporally dependent and cross-sectionally correlated. Central to our implementation is a functional analysis of variance by decomposing 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 functional analysis of variance decomposition provides an 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 point forecast accuracy by about 25% to 45% compared to an existing method, providing more transparent insights for evidence-based policy decisions, such as accurate modeling of financial costs of length of stay in the old-aged care facilities.