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.

翻译：本文提出了一种面向高维时间序列因果推断的方法论。该方法假设数据存在一个单调变换，使得变换后变量的动态可由高斯向量自回归过程描述，这等价于假设动态过程由高斯连结函数（Gaussian copula）捕捉。该方法无需了解或估计数据的边际分布，在稀疏性条件下能一致地识别描述过程动态的参数以及可能高维变量间的条件因果关系。该框架允许以有向无环图的形式识别此类因果关联。作为示例性应用，本文分析了供给侧石油冲击对经济的影响，以及由标准普尔500指数中四只成份股的限价指令簿构建的聚合变量间的因果关系。