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When dealing with time series data, causal inference methods often employstructural vector autoregressive (SVAR) processes to model time-evolving randomsystems. In this work, we rephrase recursive SVAR processes with possiblelatent component processes as a linear Structural Causal Model (SCM) ofstochastic processes on a simple causal graph, the \emph{process graph}, thatmodels every process as a single node. Using this reformulation, we generaliseWright's well-known path-rule for linear Gaussian SCMs to the newly introducedprocess SCMs and we express the auto-covariance sequence of an SVAR process bymeans of a generalised trek-rule. Employing the Fourier-Transformation, wederive compact expressions for causal effects in the frequency domain thatallow us to efficiently visualise the causal interactions in a multivariateSVAR process. Finally, we observe that the process graph can be used toformulate graphical criteria for identifying causal effects and to derivealgebraic relations with which these frequency domain causal effects can berecovered from the observed spectral density.

Formalising causal inference in time and frequency on process graphs with latent components