  The estimator of a causal directed acyclic graph (DAG) with the PC algorithm
is known to be consistent based on independent and identically distributed
samples. In this paper, we consider the scenario when the multivariate samples
are identically distributed but not independent. A common example is a
stationary multivariate time series. We show that under a standard set of
assumptions on the underlying time series involving $\rho$-mixing, the PC
algorithm is consistent in this dependent sample scenario. Further, we show
that for the popular time series models such as vector auto-regressive moving
average and linear processes, consistency of the PC algorithm holds. We also
prove the consistency for the Time-Aware PC algorithm, a recent adaptation of
the PC algorithm for the time series scenario. Our findings are supported by
simulations and benchmark real data analyses provided towards the end of the
paper.
