$\mu=(0,0,0)$ and differing cross-channel dependence structure. More specifically, the classes are defined by the three covariance matrices $$\Sigma^{(1)}=
 \begin{pmatrix}
  1 & 0 & 0.3 \\
  0 & 1 & 0.7 \\
  0.3 & 0.7 & 1
 \end{pmatrix}\!, \Sigma^{(2)}=
 \begin{pmatrix}
  1 & 0.6 & 0.1 \\
  0.6 & 1 & -0.4 \\
  0.1 & -0.4 & 1
 \end{pmatrix} \, \textrm{and}\, \Sigma^{(3)}=
 \begin{pmatrix}
  1 & -0.5 & -0.2 \\
  -0.5 & 1 & 0.1 \\
  -0.2 & 0.1 & 1
 \end{pmatrix}.$$ Example simulated data for this process using the different class switching scenarios above are shown in Figure \[fig:scen1\].

To investigate the potential of our proposed approach further, we studied an example with a time-varying moving average (VMA) process, with three classes defined by the following coefficient matrices:\
Class 1:  $
\mathbf{X}_t = \mathbf{Z}_{t} + 
 \begin{pmatrix}
  1 & 0 & 0.6 \\
  0 & 1 & 0.3 \\
  0.6 & 0.3 & 1
 \end{pmatrix} \mathbf{Z}_{t-1} + 
 \begin{pmatrix}
  1 & 0.2 & 0.9 \\
  0.2 & 1 & 0.5 \\
  0.9 & 0.5 & 1
 \end{pmatrix} \mathbf{Z}_{t-2}
$

Class 2: $ \mathbf{X}_t = \mathbf{Z}_{t} + 
 \begin{pmatrix}
  1 & -0.7 & -0.3 \\
  -0.7 & 1 & 0.4 \\
  -0.3 & 0.4 & 1
 