  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.
