Modeling the time-varying covariance structures of high-dimensional variables is critical across diverse scientific and industrial applications; however, existing approaches exhibit notable limitations in either modeling flexibility or inferential efficiency. For instance, change-point modeling fails to account for the continuous time-varying nature of covariance structures, while GARCH and stochastic volatility models suffer from over-parameterization and the risk of overfitting. To address these challenges, we propose a Bayesian factor modeling framework designed to enable simultaneous inference of both the covariance structure of a high-dimensional time series and its time-varying dynamics. The associated Expectation-Maximization (EM) algorithm not only features an exact, closed-form update for the M-step but also is easily generalizable to more complex settings, such as spatiotemporal multivariate factor analysis. We validate our method through simulation studies and real-data experiments using climate and financial datasets.

翻译：高维变量时变协方差结构的建模在众多科学与工业应用中至关重要；然而，现有方法在建模灵活性或推断效率方面均存在显著局限。例如，变点建模未能考虑协方差结构的连续时变特性，而GARCH与随机波动模型则存在参数过多和过拟合风险。为解决这些挑战，我们提出一个贝叶斯因子建模框架，旨在实现对高维时间序列协方差结构及其时变动态的同步推断。所关联的期望最大化（EM）算法不仅具有精确、闭式的M步更新，而且易于推广至更复杂的场景，如时空多元因子分析。我们通过模拟研究以及使用气候与金融数据集的实际数据实验验证了所提方法的有效性。