Causal reasoning has gained great attention over the last half century as it allows (or at least intends) to answer questions which go above those within the capabilities of classical inferential statistics using just observational data. So far, causal research has been focused mostly on the i.i.d. setting. However, many are the situations where there exists a non-trivial dependence structure between sequential observations. Motivated by this fact, the main purpose of this work is to study causal properties of time series under the structural assumption of a VARMA model with instantaneous effects. First, the global Markov property is studied, building on existing work for VAR processes without instantaneous effects. Infinite graphs which represent the dependencies of the process are defined so that separation statements translate to conditional independencies in the stationary distribution of the process. Second, faithfulness is examined as a counterpart of this Markov property. Conditions are given so that the stationary distribution of the process is almost surely faithful to said infinite graphs. In addition, an instrumental variable regression framework is developed for VARMA models with instantaneous effects. This allows to identify and consistently estimate total causal effects.

翻译：因果推理在过去半个世纪中受到极大关注，因为它允许（或至少旨在）回答那些超越经典推断统计学仅使用观测数据所能处理的问题。迄今为止，因果研究主要集中于独立同分布（i.i.d.）设定。然而，许多情况下序列观测之间存在非平凡的依赖结构。受此启发，本文的主要目的是在具有瞬时效应的VARMA模型的结构假设下，研究时间序列的因果性质。首先，基于现有针对无瞬时效应的VAR过程的研究，本文探讨了全局马尔可夫性质。定义了表示过程依赖关系的无限图，使得分离性陈述可转化为过程平稳分布中的条件独立性。其次，作为该马尔可夫性质的对偶，本文考察了忠实性。给出了使得过程平稳分布几乎必然忠实于所述无限图的条件。此外，本文为具有瞬时效应的VARMA模型开发了一个工具变量回归框架。这使得识别并一致估计总因果效应成为可能。