多维函数时间序列整合的频域方法
A Frequency-Domain Approach for Integrating Multiple Functional Time Series
AI总结：
本文提出基于边缘动态Karhunen-Loève展开的频域框架，用于整合多维函数时间序列，通过构建边缘谱算子获得最优功能滤波器，提升联合建模与估计能力。
摘要：
多变量函数时间序列（MFTS）的整合分析在许多科学领域中既关键又具有挑战性。此类数据往往表现出复杂的多维依赖关系，源于曲线内的结构、曲线间的时序相关性以及跨受试者交互，凸显了需要高效方法来同时捕捉这些依赖关系并支持准确的下游分析。本文提出了一种基于边缘动态Karhunen--Loève展开的新型频域框架。关键思想是将MFTS的个体谱密度整合起来，构建边缘谱算子，其本征函数产生最优的功能滤波器。这些滤波器将复杂的函数观测转换为结构化的多变量时间序列表示，为联合建模和估计提供了强大基础。通过广泛的模拟研究，我们展示了所提出方法的优越性能。我们进一步通过中国空气污染物浓度轨迹的插值和预测应用，验证了其实际效用。
英文摘要：
Integrative analysis of multivariate functional time series (MFTS) is both critical and challenging across many scientific domains. Such data often exhibit complex multi-way dependencies arising from within-curve structures, temporal correlations across curves, and cross-subject interactions, underscoring the need for efficient methods that can jointly capture these dependencies and support accurate downstream analyses. In this work, we propose a novel frequency-domain framework based on a marginal dynamic Karhunen--Loève expansion. The key idea is to integrate individual spectral densities of the MFTS to construct a marginal spectral operator, whose eigenfunctions yield optimal functional filters. These filters transform complex functional observations into a structured multivariate time series representation, providing a powerful foundation for joint modeling and estimation. Through extensive simulation studies, we demonstrate the superior performance of the proposed approach. We further validate its practical utility through an application to the imputation and forecasting of air pollutant concentration trajectories in China.
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