Commit bf484ed4 authored by Michel Juillard's avatar Michel Juillard
Browse files

internal documentation minor changes

parent f3bc4c25
......@@ -134,19 +134,27 @@ $\Sigma_y$.
The autocovariance matrix of $y_t$ and $y_{t-1}$ is defined as
\begin{align*}
\mbox{cov}\left(y_t,y_{t-1}\right) &=E\left\{\hat y_t\hat
y_{t-1}'\right\}\\
\mbox{cov}\left(y_t,y_{t-1}\right) &=E\left\{y_t y_{t-1}'\right\}\\
&= E\left\{\left(g_y \hat
y_{t-1}+g_u u_t\right)\hat y_{t-1}'\right\}\\
&= g_y\Sigma_y
\end{align*}
by recursion we have that $\mbox{corr}\left(y_t,y_{t-k}\right)=E_\left{y_ty_{t-k}'\right\}=g_y^k\Sigma_y$.
by recursion we have
\begin{align*}
\mbox{cov}\left(y_t,y_{t-k}\right) &=E\left\{y_t y_{t-k}'\right\} \\
&=g_y^k\Sigma_y
\end{align*}
The autocorrelation matrix is then
\[
\begin{equation*}
\mbox{corr}\left(y_t,y_{t-k}\right) =
\mbox{diag}(\sigma_y)^{-1}E_\left{y_ty_{t-k}'\right\}\mbox{diag}(\sigma_y)^{-1}
\]
\mbox{diag}\left(\sigma_y\right)^{-1}E\left\{y_ty_{t-k}'\right\}\mbox{diag}\left(\sigma_y\right)^{-1}
\end{equation*}
where $\mbox{diag}\left(\sigma_y\right)$ is a diagonal matrix with the standard deviations on the main diagonal.
*** Function <<lyapunov\_symm.m>>
- [[m2html:lyapunov_symm.html>>][M2HTML link]]
- TO BE DONE
* Estimation
** estimation
Dynare command *estimation* calls function [[dynare\_estimation.m]]
......
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