  Discovering causal relationship using multivariate functional data has
received a significant amount of attention very recently. In this article, we
introduce a functional linear structural equation model for causal structure
learning when the underlying graph involving the multivariate functions may
have cycles. To enhance interpretability, our model involves a low-dimensional
causal embedded space such that all the relevant causal information in the
multivariate functional data is preserved in this lower-dimensional subspace.
We prove that the proposed model is causally identifiable under standard
assumptions that are often made in the causal discovery literature. To carry
out inference of our model, we develop a fully Bayesian framework with suitable
prior specifications and uncertainty quantification through posterior
summaries. We illustrate the superior performance of our method over existing
methods in terms of causal graph estimation through extensive simulation
studies. We also demonstrate the proposed method using a brain EEG dataset.
