From 5d19618f46da443f1134ba8502b77c6832aedf44 Mon Sep 17 00:00:00 2001 From: Willi Mutschler Date: Wed, 21 Feb 2024 10:56:12 +0100 Subject: [PATCH] endterm exam: Fixed notation in Kalman initialization --- exam/endterm_exam_WS2324.tex | 17 ++++++++++++++--- 1 file changed, 14 insertions(+), 3 deletions(-) diff --git a/exam/endterm_exam_WS2324.tex b/exam/endterm_exam_WS2324.tex index 6cd4213..9fa26c2 100644 --- a/exam/endterm_exam_WS2324.tex +++ b/exam/endterm_exam_WS2324.tex @@ -18,8 +18,10 @@ \begin{document} \title{Quantitative Macroeconomics} -\author{Endterm Exam} +\author{Endterm Exam\\Version 1.1} \date{Winter 2023/2024} + + \maketitle \section*{General information} @@ -37,6 +39,15 @@ \section*{General information} \item If there are any questions, do not hesitate to contact Willi Mutschler. \end{itemize} +\section*{Changelog} + +\begin{itemize} + \item Version 1.1 + \begin{itemize} + \item Fixed notation in initialization step of Kalman filter to $\hat{y}_{1|0}$ and $\Sigma_{1|0}$ instead of $\hat{y}_{0|-1}$ and $\Sigma_{0|-1}$. + \end{itemize} +\end{itemize} + \newpage \section{RBC model with leisure and non-Ricardian agents} @@ -184,8 +195,8 @@ \section{Kalman filter} \paragraph{Hints:} In the lecture we have derived the necessary steps to implement the Kalman filter. \begin{itemize} -\item Initialize $\hat{y}_{0|-1}=0$ and $\Sigma_{0|-1}$ as the solution to the Lyapunov equation: -$$\Sigma_{0|-1} = g_y \Sigma_{0|-1} g_y' + g_u \Sigma_u g_u'$$ +\item Initialize $\hat{y}_{1|0}=0$ and $\Sigma_{1|0}$ as the solution to the Lyapunov equation: +$$\Sigma_{1|0} = g_y \Sigma_{1|0} g_y' + g_u \Sigma_u g_u'$$ Hint: You might want to use the auxiliary function \texttt{dlyapdoubling(gy,gu*SIGu*gu')} to solve this equation. \item For $t=1,...,T$: \begin{itemize}