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. In this paper, we introduce a new class of time series Gaussian chain graph models 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 we exploit to establish identifiability of the time series chain graph structure. Building on this, we then propose a three-stage learning procedure 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. We investigate the asymptotic properties of the proposed method, ensuring its consistency for exact recovery of the chain graph structure. The superior empirical performance of the proposed method is demonstrated through both extensive simulation studies and an application to U.S. macroeconomic data that highlights key monetary policy transmission mechanisms.

翻译：时间序列图模型近期在刻画多变量时间序列的（条件）依赖结构方面受到广泛关注。在许多应用中，多变量序列表现出变量分区的分块依赖，且块内与块间具有不同的依赖模式。本文提出一类新的时间序列高斯链图模型，该模型通过跨块的有向边表示同期与滞后因果关系，同时通过无向边捕获块内的条件依赖。在频域中，该模型对逆谱密度矩阵诱导出一种跨频率共享的群稀疏加群低秩分解，我们利用这一分解建立了时间序列链图结构的可识别性。在此基础上，我们进一步提出一个三阶段学习程序以估计无向边集与有向边集，该程序通过优化带有群套索惩罚的正则化Whittle似然来促进群稀疏性，并采用新颖的张量展开核范数惩罚来强制执行群低秩结构。我们研究了所提方法的渐近性质，确保其能够一致精确恢复链图结构。通过广泛的模拟研究以及一项突出关键货币政策传导机制的美国宏观经济数据应用，我们证明了所提方法优越的实证性能。