  In this paper, we introduce a novel class of graphical models for
representing time lag specific causal relationships and independencies of
multivariate time series with unobserved confounders. We completely
characterize these graphs and show that they constitute proper subsets of the
currently employed model classes. As we show, from the novel graphs one can
thus draw stronger causal inferences -- without additional assumptions. We
further introduce a graphical representation of Markov equivalence classes of
the novel graphs. This graphical representation contains more causal knowledge
than what current state-of-the-art causal discovery algorithms learn.
