Consistent causal inference for high-dimensional time series

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A methodology for high-dimensional causal inference in a time series context is introduced. Time series dynamics are captured by a Gaussian copula, and estimation of the marginal distribution of the data is not required. The procedure can consistently identify the parameters that describe the dynamics of the process and the conditional causal relations among the possibly high-dimensional variables, under sparsity conditions. Identification of the causal relations is in the form of a directed acyclic graph, which is equivalent to identifying the structural VAR model for the transformed variables. 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 for four stock constituents of the S&P500.