Consider the order #latex $p$ VAR representation for the $1\times m$ vector of observed variables $y_t$: \[ y_{t}=\sum_{k=1}^{p} y_{t-k} \mathbf{A}_{k} + u_t \] where $u_t\sim \mathcal N\left( 0,\Sigma_u\right)$. Let $z_t$ be the $mp\times 1$ vector $\left[ y_{t-1}',...,y_{t-p}'\right]'$ and define $\mathbf{A}=\left[\mathbf A_1',...,\mathbf A_p'\right]'$, the VAR representation can then be written in matrix form as: \[ Y=Z\mathbf A +\mathcal U \]