From bf484ed43928d44bec9360ae4b3ee2a3e4fdc288 Mon Sep 17 00:00:00 2001 From: Michel Juillard Date: Thu, 11 Nov 2010 20:48:34 +0100 Subject: [PATCH] internal documentation minor changes --- doc/internals/dynare-internals.org | 20 ++++++++++++++------ 1 file changed, 14 insertions(+), 6 deletions(-) diff --git a/doc/internals/dynare-internals.org b/doc/internals/dynare-internals.org index 5277ebed3..31cfb0912 100644 --- a/doc/internals/dynare-internals.org +++ b/doc/internals/dynare-internals.org @@ -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 <> + - [[m2html:lyapunov_symm.html>>][M2HTML link]] + - TO BE DONE * Estimation ** estimation Dynare command *estimation* calls function [[dynare\_estimation.m]]