  In this article, we propose a new hypothesis testing method for directed
acyclic graph (DAG). While there is a rich class of DAG estimation methods,
there is a relative paucity of DAG inference solutions. Moreover, the existing
methods often impose some specific model structures such as linear models or
additive models, and assume independent data observations. Our proposed test
instead allows the associations among the random variables to be nonlinear and
the data to be time-dependent. We build the test based on some highly flexible
neural networks learners. We establish the asymptotic guarantees of the test,
while allowing either the number of subjects or the number of time points for
each subject to diverge to infinity. We demonstrate the efficacy of the test
through simulations and a brain connectivity network analysis.
