  Multivariate time series (MTS) data such as time course gene expression data
in genomics are often collected to study the dynamic nature of the systems.
These data provide important information about the causal dependency among a
set of random variables. In this paper, we introduce a computationally
efficient algorithm to learn directed acyclic graphs (DAGs) based on MTS data,
focusing on learning the local structure of a given target variable. Our
algorithm is based on learning all parents (P), all children (C) and some
descendants (D) (PCD) iteratively, utilizing the time order of the variables to
orient the edges. This time series PCD-PCD algorithm (tsPCD-PCD) extends the
previous PCD-PCD algorithm to dependent observations and utilizes composite
likelihood ratio tests (CLRTs) for testing the conditional independence. We
present the asymptotic distribution of the CLRT statistic and show that the
tsPCD-PCD is guaranteed to recover the true DAG structure when the faithfulness
condition holds and the tests correctly reject the null hypotheses. Simulation
studies show that the CLRTs are valid and perform well even when the sample
sizes are small. In addition, the tsPCD-PCD algorithm outperforms the PCD-PCD
algorithm in recovering the local graph structures. We illustrate the algorithm
by analyzing a time course gene expression data related to mouse T-cell
activation.
