On learning time series DAGs: A frequency domain approach
Aramayis Dallakyan · Econometrics and Statistics · 2024
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, a novel frequency domain approach is proposed to identify a topological ordering and learn the structure of multivariate time series. In particular, a class of complex-valued Structural Causal Models (cSCM) is defined at each frequency of the Fourier transform of the time series. Assuming that the time series is generated from the transfer function model, it is demonstrated that the topological ordering and the corresponding summary directed acyclic graph can be uniquely identified from cSCM. The performance of the algorithm is investigated using simulation experiments and real datasets.