Consider the order latex($p$) VAR representation for the latex($1\times m$) vector of observed variables latex($y_t$):

\[ y_{t}=\sum_{k=1}^{p} y_{t-k} \mathbf{A}_{k} + u_t \]

where latex($u_t\sim \mathcal N\left( 0,\Sigma_u\right)$). Let latex($z_t$) be the latex($mp\times 1$) vector latex($\left[y_{t-1}',...,y_{t-p}'\right]'$) and define latex($\mathbf{A}=\left[\mathbf A_1',...,\mathbf A_p'\right]'$), the VAR representation can then be written in matrix form as:

\[ Y=Z\mathbf A +\mathcal U \]