endterm exam: Fixed notation in Kalman initialization

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}