Diff for "DsgeVar" - DynareWiki

Differences between revisions 1 and 2

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:

$Y=Z\mathbf A +\mathcal U$

-  ⇤ ← Revision 1 as of 2008-05-08 13:05:39 → 
  Size: 575
  Editor: StéphaneAdjemian
  Comment:
+   ← Revision 2 as of 2008-05-08 13:23:13 → ⇥
  Size: 682
  Editor: StéphaneAdjemian
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
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-Consider the order {{{#latex $p$}}} VAR representation for the $1\times m$ vector of observed variables
$y_t$:
+Consider the order [[latex($p$)]] VAR representation for the [[latex($1\times m$)]] vector of observed variables [[latex($y_t$)]]:
{{{#!latex
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-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:
+}}}
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:
{{{#!latex
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+}}}