  A widely applied approach to causal inference from a non-experimental time
series $X$, often referred to as "(linear) Granger causal analysis", is to
regress present on past and interpret the regression matrix $\hat{B}$ causally.
However, if there is an unmeasured time series $Z$ that influences $X$, then
this approach can lead to wrong causal conclusions, i.e., distinct from those
one would draw if one had additional information such as $Z$. In this paper we
take a different approach: We assume that $X$ together with some hidden $Z$
forms a first order vector autoregressive (VAR) process with transition matrix
$A$, and argue why it is more valid to interpret $A$ causally instead of
$\hat{B}$. Then we examine under which conditions the most important parts of
$A$ are identifiable or almost identifiable from only $X$. Essentially,
sufficient conditions are (1) non-Gaussian, independent noise or (2) no
influence from $X$ to $Z$. We present two estimation algorithms that are
tailored towards conditions (1) and (2), respectively, and evaluate them on
synthetic and real-world data. We discuss how to check the model using $X$.
