Graphical Principal Component Analysis of Multivariate Functional Time Series

In this paper, we consider multivariate functional time series with a two-way\ndependence structure: a serial dependence across time points and a graphical\ninteraction among the multiple functions within each time point. We develop the\nnotion of dynamic weak separability, a more general condition than those\nassumed in literature, and use it to characterize the two-way structure in\nmultivariate functional time series. Based on the proposed weak separability,\nwe develop a unified framework for functional graphical models and dynamic\nprincipal component analysis, and further extend it to optimally reconstruct\nsignals from contaminated functional data using graphical-level information. We\ninvestigate asymptotic properties of the resulting estimators and illustrate\nthe effectiveness of our proposed approach through extensive simulations. We\napply our method to hourly air pollution data that were collected from a\nmonitoring network in China.\n