\end{pmatrix}\! \mathbf{Z}_{t-1} + 
 \begin{pmatrix}
  1 & 0.9 & -0.3 \\
  0.9 & 1 & 0 \\
  -0.3 & 0 & 1
 \end{pmatrix}\! \mathbf{Z}_{t-2},
$

Class 3: $ \mathbf{X}_t = \mathbf{Z}_{t} + 
 \begin{pmatrix}
  1 & -0.4 & 0.2 \\
  -0.4 & 1 & -0.6 \\
  0.2 & -0.6 & 1
 \end{pmatrix}\! \mathbf{Z}_{t-1} + 
 \begin{pmatrix}
  1 & 0.1 & -0.5 \\
  0.1 & 1 & -0.3 \\
  -0.5 & -0.3 & 1
 \end{pmatrix}\! \mathbf{Z}_{t-2},
$\
where $\mathbf{Z}_{t}$, $\mathbf{Z}_{t-1}$ and $\mathbf{Z}_{t-2}$ are IID multivariate Gaussian white noise (see Figure \[fig:scen2\]).\
The third example we consider is a vector autoregressive process with intra- and cross-channel changes in dependence between each class (see Figure \[fig:scen3\]). The three classes in the example are defined by\
Class 1:  $
\mathbf{X}_t =
 \begin{pmatrix}
 0.2 & 0.3 & 0 \\
  0.3 & 0.5 & 0 \\
  0 & 0 & 0
 \end{pmatrix} \mathbf{X}_{t-1} + 
 \begin{pmatrix}
  0.6 & -0.1 & 0 \\
  -0.1 & -0.3 & 0 \\
  0 & 0 & 0
 \end{pmatrix} \mathbf{X}_{t-2} + \epsilon_{1},
$

Class 2: $ \mathbf{X}_t =
 \begin{pmatrix}
  0 & 0 & 0 \\
  0 & 0.4 & -0.4 \\
  0 & -0.4 & 0.4
 \end{pmatrix} \mathbf{X}_{t-1} + 
 \begin{pmatrix}
  0 & 0 & 0 