  A methodology for high dimensional causal inference in a time series context
is introduced. It is assumed that there is a monotonic transformation of the
data such that the dynamics of the transformed variables are described by a
Gaussian vector autoregressive process. This is tantamount to assume that the
dynamics are captured by a Gaussian copula. No knowledge or estimation of the
marginal distribution of the data is required. The procedure consistently
identifies the parameters that describe the dynamics of the process and the
conditional causal relations among the possibly high dimensional variables
under sparsity conditions. The methodology allows us to identify such causal
relations in the form of a directed acyclic graph. As illustrative applications
we consider the impact of supply side oil shocks on the economy, and the causal
relations between aggregated variables constructed from the limit order book on
four stock constituents of the S&P500.
