Figure 1.

Illustration of Granger non-causality in an example with $d=2$ and $m_1=m_2=3$. Since the tensor represents conditional probabilities, the columns of the front face of the tensor, the vertical $x_{1t}$ axis, must sum to one. Here, $x_2$ is not Granger causal for $x_1$ since each slice of the conditional probability tensor along the $x_2$ mode is equal.