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| 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: |
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: |
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Consider the order latex($p$) VAR representation for the latex($1\times m$) vector of observed variables latex($y_t$):
![\[
y_{t}=\sum_{k=1}^{p} y_{t-k} \mathbf{A}_{k} + u_t
\]](/DynareWiki/DsgeVar?action=AttachFile&do=get&target=latex_52c4e5698c537064469f092ff00bdbce8f0eaabc_p1.png "\[
y_{t}=\sum_{k=1}^{p} y_{t-k} \mathbf{A}_{k} + u_t
\]")
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:
![\[
Y=Z\mathbf A +\mathcal U
\]](/DynareWiki/DsgeVar?action=AttachFile&do=get&target=latex_be3d4da710f979cdd413f584666418601f91a3c1_p1.png "\[
Y=Z\mathbf A +\mathcal U
\]")