The fields of time series and graphical models emerged and advanced separately. Previous work on the structure learning of continuous and real-valued time series utilizes the time domain, with a focus on either structural autoregressive models or linear (non-)Gaussian Bayesian Networks. In contrast, we propose a novel frequency domain approach to identify a topological ordering and learn the structure of both real and complex-valued multivariate time series. In particular, we define a class of complex-valued Structural Causal Models (cSCM) at each frequency of the Fourier transform of the time series. Assuming that the time series is generated from the transfer function model, we show that the topological ordering and corresponding summary directed acyclic graph can be uniquely identified from cSCM. The performance of our algorithm is investigated using simulation experiments and real datasets.

翻译：时间序列与图模型领域各自独立发展并取得进展。先前针对连续实值时间序列结构学习的研究主要利用时域方法，聚焦于结构自回归模型或线性（非）高斯贝叶斯网络。相比之下，本文提出一种新颖的频域方法，用于识别拓扑序并学习实值及复值多元时间序列的结构。具体而言，我们在时间序列傅里叶变换的每个频率上定义了一类复值结构因果模型（cSCM）。假设时间序列由传递函数模型生成，我们证明可以通过cSCM唯一识别拓扑序及对应的摘要有向无环图。通过仿真实验和真实数据集验证了算法的性能。