Causal inference on process graphs: Causal structure and effect identification

A structural vector autoregressive (SVAR) process is a linear causal model for variables that evolve over a discrete set of time points and between which there may be lagged and instantaneous effects. The qualitative causal structure of an SVAR process can be represented by its finite and directed process graph, where a directed link connects two processes whenever there is a lagged or instantaneous effect between them. At the process graph level, the causal structure of SVAR processes is compactly parameterized in the frequency domain. In this paper, we consider the problem of causal discovery and causal effect estimation from the spectral density, the frequency domain analogue of the autocovariance, of the SVAR process. Causal discovery concerns the recovery of the process graph. Causal effect estimation concerns the identification and estimation of frequency domain causal effects. We show that information about the process graph, in terms of d- and t-separation, is generically characterized by algebraic constraints on the spectral density. Furthermore, we introduce a notion of rational identifiability for frequency domain causal effects between processes that may be confounded by exogenous latent processes, and show that the recent graphical latent factor half-trek criterion can be used on the process graph to assess whether a given (confounded) effect can be identified by rational operations on the entries of the spectral density.