标题： 分布的函数时间序列预测：一种Koopman-Wasserstein方法 显示英文标题

标题： Functional Time Series Forecasting of Distributions: A Koopman-Wasserstein Approach

摘要： 我们提出了一种新的方法，用于预测在离散时间点观察到的概率分布的时序演变。 扩展动态概率密度分解（DPDD），我们通过Koopman算子框架将分布动力学嵌入到Wasserstein几何中。 我们的方法引入了扩展动态模式分解（EDMD）的重要性加权变体，使得在2-Wasserstein空间中能够进行准确的闭式预测。 理论保证已建立：我们的估计器实现了谱收敛和最优有限样本Wasserstein误差。 模拟研究和一个对美国住房价格分布的真实应用表明，与现有的Wasserstein自回归等方法相比有显著改进。 通过整合最优传输、函数时间序列建模和谱算子理论，DPDD为分布预测提供了一个可扩展且可解释的解决方案。 这项工作在行为科学、公共卫生、金融和神经成像等领域具有广泛的意义——这些领域中演化的分布自然出现。 我们的框架有助于非欧几里得空间上的函数数据分析，并为建模和预测分布时间序列提供了一个通用工具。 显示英文摘要

摘要： We propose a novel method for forecasting the temporal evolution of probability distributions observed at discrete time points. Extending the Dynamic Probability Density Decomposition (DPDD), we embed distributional dynamics into Wasserstein geometry via a Koopman operator framework. Our approach introduces an importance-weighted variant of Extended Dynamic Mode Decomposition (EDMD), enabling accurate, closed-form forecasts in 2-Wasserstein space. Theoretical guarantees are established: our estimator achieves spectral convergence and optimal finite-sample Wasserstein error. Simulation studies and a real-world application to U.S. housing price distributions show substantial improvements over existing methods such as Wasserstein Autoregression. By integrating optimal transport, functional time series modeling, and spectral operator theory, DPDD offers a scalable and interpretable solution for distributional forecasting. This work has broad implications for behavioral science, public health, finance, and neuroimaging--domains where evolving distributions arise naturally. Our framework contributes to functional data analysis on non-Euclidean spaces and provides a general tool for modeling and forecasting distributional time series.