internal documentation minor changes
parent
f3bc4c2564
commit
bf484ed439
|
@ -134,19 +134,27 @@ $\Sigma_y$.
|
||||||
|
|
||||||
The autocovariance matrix of $y_t$ and $y_{t-1}$ is defined as
|
The autocovariance matrix of $y_t$ and $y_{t-1}$ is defined as
|
||||||
\begin{align*}
|
\begin{align*}
|
||||||
\mbox{cov}\left(y_t,y_{t-1}\right) &=E\left\{\hat y_t\hat
|
\mbox{cov}\left(y_t,y_{t-1}\right) &=E\left\{y_t y_{t-1}'\right\}\\
|
||||||
y_{t-1}'\right\}\\
|
|
||||||
&= E\left\{\left(g_y \hat
|
&= E\left\{\left(g_y \hat
|
||||||
y_{t-1}+g_u u_t\right)\hat y_{t-1}'\right\}\\
|
y_{t-1}+g_u u_t\right)\hat y_{t-1}'\right\}\\
|
||||||
&= g_y\Sigma_y
|
&= g_y\Sigma_y
|
||||||
\end{align*}
|
\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
|
The autocorrelation matrix is then
|
||||||
\[
|
\begin{equation*}
|
||||||
\mbox{corr}\left(y_t,y_{t-k}\right) =
|
\mbox{corr}\left(y_t,y_{t-k}\right) =
|
||||||
\mbox{diag}(\sigma_y)^{-1}E_\left{y_ty_{t-k}'\right\}\mbox{diag}(\sigma_y)^{-1}
|
\mbox{diag}\left(\sigma_y\right)^{-1}E\left\{y_ty_{t-k}'\right\}\mbox{diag}\left(\sigma_y\right)^{-1}
|
||||||
\]
|
\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
|
||||||
** estimation
|
** estimation
|
||||||
Dynare command *estimation* calls function [[dynare\_estimation.m]]
|
Dynare command *estimation* calls function [[dynare\_estimation.m]]
|
||||||
|
|
Loading…
Reference in New Issue