A1634
Title: Time series Gaussian chain graph models
Authors: Qin Fang - The University of Sydney (Australia) [presenting]
Xinghao Qiao - The University of Hong Kong (Hong Kong)
Zihan Wang - Tsinghua University (China)
Abstract: Time series graphical models have recently received considerable attention for characterizing conditional dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned blockwise dependence, with distinct patterns within and across blocks. A new class of time series Gaussian chain graph models is introduced that represent contemporaneous and lagged causal relations via directed edges across blocks, while capturing within-block conditional dependencies through undirected edges. In the frequency domain, this formulation induces a cross-frequency shared group sparse plus group low-rank decomposition of the inverse spectral density matrices, which is exploited to establish identifiability of the time series chain graph structure. Building on this, a three-stage learning procedure is proposed for estimating the undirected and directed edge sets, which involves optimizing a regularized Whittle likelihood with a group lasso penalty to encourage group sparsity and a novel tensor-unfolding nuclear norm penalty to enforce group low-rank structure. The asymptotic properties of the proposed method are investigated, ensuring its consistency for exact recovery of the chain graph structure. Superior empirical performance is demonstrated through both extensive simulation studies and an application to U.S. macroeconomic data that highlights key monetary policy transmission mechanisms.
