From fbc74afa3d336cce90f352143aebec2b48cc26fb Mon Sep 17 00:00:00 2001
From: Willi Mutschler <willi@mutschler.eu>
Date: Thu, 17 Oct 2024 16:14:27 +0200
Subject: [PATCH] Added week 2 materials

---
 .../dynare-6.2-matlab-r2024b-macos.yml        | 11 +++
 .../dynare-6.2-matlab-r2024b-ubuntu.yml       | 11 +++
 .../dynare-6.2-matlab-r2024b-windows.yml      | 10 +++
 README.md                                     |  4 +-
 ...efinition_frequencies_time_series_data.tex | 11 ++-
 ..._frequencies_time_series_data_solution.tex | 18 ++---
 ...mental_concepts_univariate_time_series.tex | 36 ++++++----
 ...ncepts_univariate_time_series_solution.tex | 68 ++++++++++---------
 exercises/visualizing_time_series_data.tex    | 18 ++---
 .../visualizing_time_series_data_solution.tex | 37 +++++-----
 week_2.tex                                    | 30 ++++++++
 11 files changed, 163 insertions(+), 91 deletions(-)
 create mode 100644 week_2.tex

diff --git a/.github/workflows/dynare-6.2-matlab-r2024b-macos.yml b/.github/workflows/dynare-6.2-matlab-r2024b-macos.yml
index 3352230..f2fd603 100644
--- a/.github/workflows/dynare-6.2-matlab-r2024b-macos.yml
+++ b/.github/workflows/dynare-6.2-matlab-r2024b-macos.yml
@@ -42,3 +42,14 @@ jobs:
             addpath("Dynare-6.2-arm64/matlab");
             cd("progs/matlab");
             quickTourMatlab;
+
+      - name: Run week 2 codes
+        uses: matlab-actions/run-command@v2
+        with:
+          command: |
+            addpath("Dynare-6.2-arm64/matlab");
+            cd("progs/matlab");
+            visualizingTimeSeriesDataNorway;
+            definitionFrequenciesTimeSeriesData;
+            whiteNoisePlots;
+            plotsAR1;
diff --git a/.github/workflows/dynare-6.2-matlab-r2024b-ubuntu.yml b/.github/workflows/dynare-6.2-matlab-r2024b-ubuntu.yml
index 152891d..a5a0f47 100644
--- a/.github/workflows/dynare-6.2-matlab-r2024b-ubuntu.yml
+++ b/.github/workflows/dynare-6.2-matlab-r2024b-ubuntu.yml
@@ -71,3 +71,14 @@ jobs:
             addpath("dynare/matlab");
             cd("progs/matlab");
             quickTourMatlab;
+
+      - name: Run week 2 codes
+        uses: matlab-actions/run-command@v2
+        with:
+          command: |
+            addpath("dynare/matlab");
+            cd("progs/matlab");
+            visualizingTimeSeriesDataNorway;
+            definitionFrequenciesTimeSeriesData;
+            whiteNoisePlots;
+            plotsAR1;
diff --git a/.github/workflows/dynare-6.2-matlab-r2024b-windows.yml b/.github/workflows/dynare-6.2-matlab-r2024b-windows.yml
index 6c3481e..64ef52b 100644
--- a/.github/workflows/dynare-6.2-matlab-r2024b-windows.yml
+++ b/.github/workflows/dynare-6.2-matlab-r2024b-windows.yml
@@ -34,3 +34,13 @@ jobs:
             cd("progs/matlab");
             quickTourMatlab;
 
+      - name: Run week 2 codes
+        uses: matlab-actions/run-command@v2
+        with:
+          command: |
+            addpath("D:\hostedtoolcache\windows\dynare-6.0\matlab");
+            cd("progs/matlab");
+            visualizingTimeSeriesDataNorway;
+            definitionFrequenciesTimeSeriesData;
+            whiteNoisePlots;
+            plotsAR1;
diff --git a/README.md b/README.md
index 62ad82b..e735438 100644
--- a/README.md
+++ b/README.md
@@ -42,7 +42,6 @@ Please feel free to use this for teaching or learning purposes; however, taking
 
 </details>
 
-<!---
 
 <details>
   <summary>Week 2: Time series data and fundamental concepts</summary>
@@ -67,6 +66,9 @@ Please feel free to use this for teaching or learning purposes; however, taking
 
 </details>
 
+<!---
+
+
 <details>
   <summary>Week 3: Dependent time series data and the autoregressive process</summary>
 
diff --git a/exercises/definition_frequencies_time_series_data.tex b/exercises/definition_frequencies_time_series_data.tex
index a9df373..3609aa9 100644
--- a/exercises/definition_frequencies_time_series_data.tex
+++ b/exercises/definition_frequencies_time_series_data.tex
@@ -13,20 +13,19 @@
 		\item \texttt{NorwayUnemploymentRate.xls}
 	\end{itemize}
 	Open the individual files and make note of the structure and source of the data.
-	Import the data and replicate figure \ref{fig:NorwayData}.
+	Import the data and replicate figure~\ref{fig:NorwayData}.
 	   \begin{figure}[htbp]
 		\centering
 		\includegraphics[width=\linewidth]{plots/NorwayDataOverviewMatlab.pdf}
-		\caption{Various Time Series For Norway}
-		\label{fig:NorwayData}
+		\caption{Various Time Series For Norway}\label{fig:NorwayData}
 		\end{figure}
    \item What are the data frequencies for each time series?
    For what kind of economic analysis would you use these frequencies?
    \item What are the sample sizes?
    From an economic and/or statistical point of view, is it always better to have a larger sample size?
    \item Roughly speaking, a time series consists of four components: a trend, a cycle, a season, and noise.
-   To what extent do you find these features in figure \ref{fig:NorwayData}?
-   \item Consider the plots in figure \ref{fig:NorwayData} jointly.
+   To what extent do you find these features in figure~\ref{fig:NorwayData}?
+   \item Consider the plots in figure~\ref{fig:NorwayData} jointly.
    What are possible macroeconomic issues that could be analyzed?
    \item How do you aggregate time series of stock variables (like capital or debt) and of flow variables (like GDP)?
    For example, if you have monthly data, how do you get a quarterly time series?
@@ -38,7 +37,7 @@
 \end{itemize}
 
 \begin{solution}\textbf{Solution to \nameref{ex:DefinitionFrequenciesTimeSeriesData}}
-\ifDisplaySolutions
+\ifDisplaySolutions%
 \input{exercises/definition_frequencies_time_series_data_solution.tex}
 \fi
 \newpage
diff --git a/exercises/definition_frequencies_time_series_data_solution.tex b/exercises/definition_frequencies_time_series_data_solution.tex
index 7d92da4..4f6f662 100644
--- a/exercises/definition_frequencies_time_series_data_solution.tex
+++ b/exercises/definition_frequencies_time_series_data_solution.tex
@@ -1,9 +1,9 @@
 \begin{enumerate}
-\item A time series is a collection of observations $Y_t$ indexed by the date of each observation $t$.
-For simplicity often one denotes $t=0,1,2,...,T$,
-  then $\{Y_t\}_0^T = \{Y_0,Y_1,Y_2,...,Y_T\}$ is a sequence of random variables ordered in time
-  (each $Y_t$ is a random variable), which we call a stochastic process.
-Sometimes we rely on the concept of an infinite sample and consider $\{Y_t\}_{t=-\infty}^\infty$ or simply $\{Y_t\}$.
+\item A time series is a collection of observations \(Y_t\) indexed by the date of each observation \(t\).
+For simplicity often one denotes \(t=0,1,2,\ldots ,T\),
+  then \( {\{Y_t\}}_0^T = \{Y_0,Y_1,Y_2,\ldots ,Y_T\} \) is a sequence of random variables ordered in time
+  (each \(Y_t\) is a random variable), which we call a stochastic process.
+Sometimes we rely on the concept of an infinite sample and consider \( {\{Y_t\}}_{t=-\infty}^\infty \) or simply \( \{Y_t\} \).
 A stochastic process can have many outcomes, due to its randomness,
   and a single outcome of a stochastic process is called a sample function or realization.
 A time series model assigns a joint probability distribution to the stochastic process.
@@ -56,7 +56,9 @@
         \item Are house prices in line with their fundamentals? Is there a bubble?
     \end{itemize}
 \item Aggregation of higher frequencies to lower frequencies is straightforward;
-  that is, for stock variables (such as capital or debt) we simply take the value observed, i.e. $k_t^{Q1} = k_t^{m3}$,
-  whereas for flow variables (such as GDP) we can take the mean: $y_t^{Q1} = 1/3 (y_t^{m1}+y_t^{m2}+y_t^{m3})$.
-Disaggregation is much more difficult and we need to use tools like interpolation or spline functions etc. $\rightarrow$ not straightforward!
+  that is, for stock variables (such as capital or debt) we simply take the value observed, i.e.\
+  \(k_t^{Q1} = k_t^{m3}\),
+  whereas for flow variables (such as GDP) we can take the mean: \(y_t^{Q1} = 1/3 (y_t^{m1}+y_t^{m2}+y_t^{m3})\).
+Disaggregation is much more difficult and we need to use tools like interpolation or spline functions etc.\
+  \(\rightarrow \) not straightforward!
 \end{enumerate}
\ No newline at end of file
diff --git a/exercises/fundamental_concepts_univariate_time_series.tex b/exercises/fundamental_concepts_univariate_time_series.tex
index fdb2b2c..4de9cf6 100644
--- a/exercises/fundamental_concepts_univariate_time_series.tex
+++ b/exercises/fundamental_concepts_univariate_time_series.tex
@@ -1,27 +1,35 @@
 \section[Some Fundamental Concepts Of Univariate Time Series Analysis]{Some Fundamental Concepts Of Univariate Time Series Analysis\label{ex:FundamentalConceptsUnivariateTimeSeriesAnalysis}}
 
 \begin{enumerate}
-	\item Define the \enquote{White Noise Process} labeled shortly as $\varepsilon_t \sim WN(0,\sigma_\varepsilon^2)$.
-	\item Plot 200 observations of 
-	\begin{align*} 
-		   (i)~y_t  &= \varepsilon_t
-		\\ (ii)~y_t &= \frac{1}{5}(\varepsilon_{t-2}+\varepsilon_{t-1}+\varepsilon_{t}+\varepsilon_{t+1}+\varepsilon_{t+2})
-	\end{align*} 
-	with $\varepsilon_{t} \sim N(0,1)$. What are the differences?	
-	\item Briefly explain the concepts of (i) weak stationarity and (ii) strict stationarity.
-	\item Define the autocovariance and autocorrelation function for a covariance-stationary stochastic process $\{Y_t\}$.
-	\item Consider the linear first-order difference equation $$y_t=\phi y_{t-1}+\varepsilon_t$$ with $\varepsilon_{t} \sim N(0,1)$. Simulate and plot 200 observations of $(i) |\phi|<1$, $(ii) \phi=1$, and $(iii) |\phi| >1$. What does this imply in terms of stationarity of the process?
-	\item Briefly explain the Lag-operator and Lag-polynomials. How can we check whether an AR(p) process $$y_t - \phi_1 y_{t-1} -\phi_2 y_{t-2} - ... - \phi_p y_{t-p} = (1-\phi_1 L-\phi_2 L^2 -... - \phi_p L^p)y_t = \varepsilon_t$$ is weakly stationary?
+\item Define the \enquote{White Noise Process} labeled shortly as \(\varepsilon_t \sim WN(0,\sigma_\varepsilon^2)\).
+\item Plot 200 observations of 
+\begin{align*} 
+(i)~y_t  &= \varepsilon_t
+\\
+(ii)~y_t &= \frac{1}{5}(\varepsilon_{t-2}+\varepsilon_{t-1}+\varepsilon_{t}+\varepsilon_{t+1}+\varepsilon_{t+2})
+\end{align*} 
+with \(\varepsilon_{t} \sim N(0,1)\). What are the differences?	
+\item Briefly explain the concepts of (i) weak stationarity and (ii) strict stationarity.
+\item Define the autocovariance and autocorrelation function for a covariance-stationary stochastic process \( \{Y_t\} \).
+\item Consider the linear first-order difference equation
+\[y_t=\phi y_{t-1}+\varepsilon_t\]
+  with \(\varepsilon_{t} \sim N(0,1)\).
+Simulate and plot 200 observations of \((i) |\phi|<1\), \((ii) \phi=1\), and \((iii) |\phi| >1\).
+What does this imply in terms of stationarity of the process?
+\item Briefly explain the Lag-operator and Lag-polynomials.
+How can we check whether an {AR{(p)}} process
+\[y_t - \phi_1 y_{t-1} -\phi_2 y_{t-2} - \cdots  - \phi_p y_{t-p} = (1-\phi_1 L-\phi_2 L^2 -\cdots  - \phi_p L^p)y_t = \varepsilon_t\]
+is weakly stationary?
 \end{enumerate}
 
 \paragraph{Readings}
 \begin{itemize}
-	\item \textcite[Ch.2]{Bjornland.Thorsrud_2015_AppliedTimeSeries}	
-	\item \textcite{Lutkepohl_2004_UnivariateTimeSeries}	
+\item \textcite[Ch.2]{Bjornland.Thorsrud_2015_AppliedTimeSeries}
+\item \textcite{Lutkepohl_2004_UnivariateTimeSeries}
 \end{itemize}
 
 \begin{solution}\textbf{Solution to \nameref{ex:FundamentalConceptsUnivariateTimeSeriesAnalysis}}
-\ifDisplaySolutions
+\ifDisplaySolutions%
 \input{exercises/fundamental_concepts_univariate_time_series_solution.tex}
 \fi
 \newpage
diff --git a/exercises/fundamental_concepts_univariate_time_series_solution.tex b/exercises/fundamental_concepts_univariate_time_series_solution.tex
index e569c17..2dcfa04 100644
--- a/exercises/fundamental_concepts_univariate_time_series_solution.tex
+++ b/exercises/fundamental_concepts_univariate_time_series_solution.tex
@@ -1,62 +1,64 @@
 \begin{enumerate}
-\item A white noise has mean zero, a constant variance and all other second-order moments (i.e. autocovariances/autocorrelations) are zero:
+\item A white noise has mean zero, a constant variance and all other second-order moments (i.e.\ autocovariances/autocorrelations) are zero:
 \begin{align*}
     E[\varepsilon_t]&=0\\
     Var[\varepsilon_t]&=E[\varepsilon_t^2] - E[\varepsilon_t]E[\varepsilon_t] = \sigma_\varepsilon^2\\
-    Cov(\varepsilon_{t},\varepsilon_s) &= E[\varepsilon_t \varepsilon_s] - E[\varepsilon_t]E[\varepsilon_s] = 0 \text{ for $s \neq t$}
+    Cov(\varepsilon_{t},\varepsilon_s) &= E[\varepsilon_t \varepsilon_s] - E[\varepsilon_t]E[\varepsilon_s] = 0~\text{for}~s \neq t
 \end{align*}	
 \item \lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily,title=\lstname]{progs/matlab/whiteNoisePlots.m}
-Every simulation is different, model can thus generate an infinite set of realizations over the period $t=1,...,200$.
+Every simulation is different, model can thus generate an infinite set of realizations over the period \(t=1,\ldots ,200\).
 The processes do differ in their persistence.
 (i) is the white noise process, which is not persistent.
 (ii) is a 5-point-moving-average, which is a linear combination of white noise processes.
 It is smoother and more persistent and very different from just noise.
 Linear combinations of white noise processes build the basis of many models in time series analysis.
-\item A process is said to be \textbf{$N$-order weakly stationary} if all its joint moments up to order $N$ exist and are time invariant.
-We are particularly interested in $N=2$, i.e. \textbf{covariance stationarity}:
+\item A process is said to be \textbf{\(N\)-order weakly stationary} if all its joint moments up to order \(N\) exist and are time invariant.
+We are particularly interested in \(N=2\), i.e.\ \textbf{covariance stationarity}:
 \begin{align*}
-E[Y_t]&=\mu \text{ (constant for all t)}
+E[Y_t]&=\mu~\text{(constant for all t)}
 \\
-Var[Y_t]&=E[(Y_t - \mu)(Y_t-\mu)]=\gamma_0 \text{ (constant for all t)}
+Var[Y_t]&=E[(Y_t - \mu)(Y_t-\mu)]=\gamma_0~\text{(constant for all t)}
 \\
-Cov[Y_{t_1},Y_{t_1-k}] &= E[(Y_{t_1}-\mu)(Y_{t_1-k}-\mu)] = Cov[Y_{t_2},Y_{t_2-k}] = \gamma_k  \text{ (only dependent on $k$)}
+Cov[Y_{t_1},Y_{t_1-k}] &= E[(Y_{t_1}-\mu)(Y_{t_1-k}-\mu)] = Cov[Y_{t_2},Y_{t_2-k}] = \gamma_k~\text{(only dependent on \(k\))}
 \end{align*}
-That is the first two moments are not dependent on $t$.
-Particularly, the autocovariance is only dependent on the time difference $k$, but not on the actual point in time $t$.
+That is the first two moments are not dependent on \(t\).
+Particularly, the autocovariance is only dependent on the time difference \(k\), but not on the actual point in time \(t\).
 \\
-\textbf{Strict stationarity}: for all $k$ and $h$: $$f(Y_t,Y_{t-1},...,Y_{t-k})=f(Y_{t-h},Y_{t-h-1},...,Y_{t-h-k})$$
-That is, not only the first two moments but the whole distribution is not dependent on the point in time $t$,
-  but on the time difference $k$.
+\textbf{Strict stationarity}: for all \(k\) and \(h\):
+\[f(Y_t,Y_{t-1},\ldots ,Y_{t-k})=f(Y_{t-h},Y_{t-h-1},\ldots ,Y_{t-h-k})\]
+That is, not only the first two moments but the whole distribution is not dependent on the point in time \(t\),
+  but on the time difference \(k\).
 \item Autocovariance function for a covariance-stationary process:
-$$\gamma_k = E[(Y_t - \mu)(Y_{t-k}-\mu)]$$
-where $\gamma_0$ is the variance. Autocorrelation function: $$\rho_k = \gamma_k/\gamma_0$$
-\\	
+\[\gamma_k = E[(Y_t - \mu)(Y_{t-k}-\mu)]\]
+where \(\gamma_0\) is the variance. Autocorrelation function: \[\rho_k = \gamma_k/\gamma_0\]
+\\
 We can estimate this by using:
 \begin{align*}
-    \hat{\gamma}_k = c_k &= \frac{1}{T} \sum_{t=k+1}^T(y_t -\bar{y})(y_{t-k}-\bar{y})\\
-    \hat{\rho}_k = r_k & = c_k/c_0
-    \end{align*}
+\hat{\gamma}_k = c_k &= \frac{1}{T} \sum_{t=k+1}^T(y_t -\bar{y})(y_{t-k}-\bar{y})
+\\
+\hat{\rho}_k = r_k & = c_k/c_0
+\end{align*}
 Note: In most applications we don't correct the degrees of freedom for numerical reasons
-  (e.g. to avoid singularity of autocovariance matrices in the multivariate case),
-  i.e. the sums are not divided by $T-k-1$ but simply by $T$.
-For $T>100$ this does not really matter as the expressions are very close to each other.
+  (e.g.\ to avoid singularity of autocovariance matrices in the multivariate case),
+  i.e.\ the sums are not divided by \(T-k-1\) but simply by \(T\).
+For \(T>100\) this does not really matter as the expressions are very close to each other.
 
 \item \lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily,title=\lstname]{progs/matlab/plotsAR1.m}
-Remarks: If $|\phi|<1$ the series returns to the mean, i.e. it is stable and stationary.
-If $|\phi>1|$ then it explodes, i.e. it is unstable and not stationary.
-$\phi=1$ is a so-called random walk,
+Remarks: If \(|\phi|<1\) the series returns to the mean, i.e.\ it is stable and stationary.
+If \(|\phi>1|\) then it explodes, i.e.\ it is unstable and not stationary.
+\(\phi=1\) is a so-called random walk,
   it is the key model when working with non-stationary models.
 Note that the random walk incorporates many different shapes, in macroeconomic forecasts we often want to \textbf{beat} the random walk model.
 \item It is a special LINEAR operator, similar to the expectation operator, and very useful when working with time series.
-The operator transforms one time series into another by shifting the observation from period $t$ to period $t-1$:
-$Ly_t = y_{t-1}$ or $L^{-1} y_t =y_{t+1}$.
-More general: $L^k y_t = L^{k-1} L y_t = L^{k-1} y_{t-1} = ... = y_{t-k}$.
+The operator transforms one time series into another by shifting the observation from period \(t\) to period \(t-1\):
+\(Ly_t = y_{t-1}\) or \(L^{-1} y_t =y_{t+1}\).
+More general: \(L^k y_t = L^{k-1} L y_t = L^{k-1} y_{t-1} = \cdots  = y_{t-k}\).
 Convenient use:
-$$(1-L)y_t = y_t - y_{t-1}= \Delta y_t$$
+\[(1-L)y_t = y_t - y_{t-1}= \Delta y_t\]
 We can also work with lag-polynomials:
-$$ \phi(L) = (1-\phi_1 L-\phi_2 L^2 -... - \phi_p L^p)$$
+\[ \phi(L) = (1-\phi_1 L-\phi_2 L^2 -\cdots  - \phi_p L^p)\]
 where we call p the lag order. So:
-$$ \phi(L) y_t = (1-\phi_1 L-\phi_2 L^2 -... - \phi_p L^p)y_t = y_t - \phi_1 y_{t-1} -\phi_2 y_{t-2} - ... - \phi_p y_{t-p}$$
-To check whether an AR(p) model is covariance stationarity, we need to check whether the roots of the lag-polynomial lie outside the unit circle.
-That is, we treat $L$ as a complex number $z\in \mathbb{C}$ and compute the roots of $(1-\phi_1 z-\phi_2 z^2 -... - \phi_p z^p)=0$ (using a computer in most cases).
+\[ \phi(L) y_t = (1-\phi_1 L-\phi_2 L^2 -\cdots  - \phi_p L^p)y_t = y_t - \phi_1 y_{t-1} -\phi_2 y_{t-2} - \cdots  - \phi_p y_{t-p}\]
+To check whether an {AR{(p)}} model is covariance stationarity, we need to check whether the roots of the lag-polynomial lie outside the unit circle.
+That is, we treat \(L\) as a complex number \(z\in \mathbb{C}\) and compute the roots of \((1-\phi_1 z-\phi_2 z^2 -\cdots  - \phi_p z^p)=0\) (using a computer in most cases).
 \end{enumerate}
\ No newline at end of file
diff --git a/exercises/visualizing_time_series_data.tex b/exercises/visualizing_time_series_data.tex
index a77bb77..00270e1 100644
--- a/exercises/visualizing_time_series_data.tex
+++ b/exercises/visualizing_time_series_data.tex
@@ -27,22 +27,22 @@
 
 \paragraph{Readings}
 \begin{itemize}
-	\item \url{https://de.mathworks.com/help/matlab/import_export/import-data-interactively.html}
-	\item \url{https://de.mathworks.com/help/matlab/import_export/select-spreadsheet-data-interactively.html}
-	\item \textcite[Ch.2]{Bjornland.Thorsrud_2015_AppliedTimeSeries}	
+\item {\footnotesize\url{https://de.mathworks.com/help/matlab/import_export/import-data-interactively.html}}
+\item {\footnotesize\url{https://de.mathworks.com/help/matlab/import_export/select-spreadsheet-data-interactively.html}}
+\item \textcite[Ch.2]{Bjornland.Thorsrud_2015_AppliedTimeSeries}
 \end{itemize}
 
 \paragraph{Useful resources}
 \begin{itemize}	
-	\item Economic Data Resources (\url{https://libguides.umn.edu/c.php?g=843682&p=6527336})
-	\item Gould Library - The Data Search (\url{https://gouldguides.carleton.edu/c.php?g=147179&p=965273})
-	\item DBNomics Providers (\url{https://db.nomics.world/providers})
-	\item Our World in Data (\url{https://ourworldindata.org})
-	\item FRED (\url{https://fred.stlouisfed.org})
+\item Economic Data Resources (\url{https://libguides.umn.edu/c.php?g=843682&p=6527336})
+\item Gould Library {-} The Data Search (\url{https://gouldguides.carleton.edu/c.php?g=147179&p=965273})
+\item DBNomics Providers (\url{https://db.nomics.world/providers})
+\item Our World in Data (\url{https://ourworldindata.org})
+\item FRED (\url{https://fred.stlouisfed.org})
 \end{itemize}
 
 \begin{solution}\textbf{Solution to \nameref{ex:VisualizingTimeSeriesData}}
-\ifDisplaySolutions
+\ifDisplaySolutions%
 \input{exercises/visualizing_time_series_data_solution.tex}
 \fi
 \newpage
diff --git a/exercises/visualizing_time_series_data_solution.tex b/exercises/visualizing_time_series_data_solution.tex
index ef0460b..722e5a3 100644
--- a/exercises/visualizing_time_series_data_solution.tex
+++ b/exercises/visualizing_time_series_data_solution.tex
@@ -18,7 +18,7 @@
         \end{itemize}
     \item US-centric sources: 
         \begin{itemize}
-            \item FRED database: User-friendly database of U.S. and \textbf{international} time series data maintained by the Federal Reserve Bank of St. Louis
+            \item FRED database: User-friendly database of U.S. and \textbf{international} time series data maintained by the Federal Reserve Bank of St.\ Louis
             \item Bureau of Labor Statistics (BLS): publishes data on unemployment and consumer prices, as well as a host of data related to the U.S. labor force
             \item Bureau of Economic Analysis (BEA): compiles extensive data on gross domestic product (GDP), personal income, and corporate profits
             \item National Bureau of Economic Research (NBER): hosts data covering the U.S. economy, industry, and international trade
@@ -27,7 +27,7 @@
     \item Worldwide:
         \begin{itemize}
             \item Central or national banks maintain many macroeconomic statistics
-            \item World Bank maintains many large datasets across most countries,
+            \item World Bank maintains many datasets across most countries,
               including the World Development Indicators (WDI) database
               and the Global Financial Development Database (GFDD).
             While they maintain an extensive set of data series with expansive country coverage,
@@ -44,21 +44,21 @@
             \item DB NOMICS
             \item Datastream and EIKON
             \item Macrobond
-        \end{itemize}		
+        \end{itemize}
 	\end{itemize}
 \item It all depends on the analysis you want to conduct,
-  i.e. whether you need country-, sector- or firm-specific data.
+  i.e.\ whether you need country-, sector- or firm-specific data.
 Try to get a name for a category the dataset might belong to.
 Tipp: Go through the list of Providers on DBNomics to see which categories there are.
 Our World in Data also tends to give good ideas where to get data from.
 Always try official sources first,
-  i.e. national statistical offices or central banks,
-  then large international organizations, i.e. World Bank, OECD or BIS.
+  i.e.\ national statistical offices or central banks,
+  then large international organizations, i.e.\ World Bank, {OECD} or {BIS}.
 Also when reading other papers, have a close look which sources have been used.
 \item
-The data was downloaded on October 26, 2022 from FRED and saved into a CSV (comma-seperated values) file \texttt{NorwayGDP.csv}.
+The data was downloaded on October 26, 2022 from FRED and saved into a CSV (comma-separated values) file \texttt{NorwayGDP.csv}.
 The shortcode is \texttt{CLVMNACSCAB1GQNO}: Real Gross Domestic Product for Norway, Millions of Chained 2010 National Currency, Quarterly, Seasonally Adjusted.
-The time period included is 1978-01-01 to 2022-04-01.
+The time period included is {1978--01--01} to {2022--04--01}.
 Use MATLAB's \texttt{Import Data} feature and select the columns and rows of the data.
 Edit the names of the variables and the input format of the dates;
   it is useful to tell MATLAB that the column for dates are actual dates,
@@ -69,24 +69,21 @@
 \lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily,title=\lstname]{progs/matlab/visualizingTimeSeriesDataNorway.m}
 Remarks:
 \begin{itemize}
-    \item A growth rate can be approximated using logs $$\frac{Y_t - Y_{t-p}}{Y_{t-p}} \approx log \left(\frac{Y_t}{Y_{t-p}}\right)$$
-      where $p=1$ would correspond to one period lagged. If we want to compute year-on-year rates we would set $p=4$ for quarterly data.
-    \item Normal distribution is not a very good choice, as we have asymmetry and some probability mass in the tails of the distribution.		
+\item A growth rate can be approximated using logs
+\[\frac{Y_t - Y_{t-p}}{Y_{t-p}} \approx \log \left(\frac{Y_t}{Y_{t-p}}\right)\]
+where \(p=1\) would correspond to one period lagged. If we want to compute year-on-year rates we would set \(p=4\) for quarterly data.
+\item Normal distribution is not a very good choice, as we have asymmetry and some probability mass in the tails of the distribution.
 \end{itemize}
 \item See above for the code. The distributions differ significantly depending on the subsample considered.
 The assumption of normality is violated; thus, we are faced with skewed distributions and have to deal with possible outliers.
-This is very typical for macroeconomic time series data, see e.g. \textcite{Ascari.Fagiolo.Roventini_2015_FatTailDistributionsBusinessCycle} or \textcite{Fagiolo.Napoletano.Roventini_2008_AreOutputGrowthrate}.
+This is very typical for macroeconomic time series data, see e.g.\ \textcite{Ascari.Fagiolo.Roventini_2015_FatTailDistributionsBusinessCycle} or \textcite{Fagiolo.Napoletano.Roventini_2008_AreOutputGrowthrate}.
 However, we will see that during the course we will still keep the normality assumption;
   so keep this in mind for later whether this is correct or not.
 \item Optional:
 \begin{itemize}
-    \item Clone the repository.
-    \item Download data for e.g. Germany and put that into \texttt{data/GermanyGDP.csv}
-    \item Create a MATLAB script with your codes under \texttt{progs/matlab/visualizingTimeSeriesDataGermany.m}
-    \item Uncomment the line at the end of \texttt{exercises/visualizing\_time\_series\_data\_solution.inc},
-    so that your script is included in the compiled PDF.    
-    \item Do a pull request on GitHub.
+\item Clone the repository.
+\item Download data for e.g. Germany and put that into \texttt{data/GermanyGDP.csv}
+\item Create a MATLAB script with your codes under\\\texttt{progs/matlab/visualizingTimeSeriesDataGermany.m}
+\item Do a pull request on GitHub.
 \end{itemize}
-%% Uncomment (i.e. remove the %) from the following line for your pull request, change the names accordingly.
-%\lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily,title=\lstname]{progs/matlab/visualizingTimeSeriesDataGermany.m}
 \end{enumerate}
\ No newline at end of file
diff --git a/week_2.tex b/week_2.tex
new file mode 100644
index 0000000..36120b9
--- /dev/null
+++ b/week_2.tex
@@ -0,0 +1,30 @@
+% !TEX root = week_2.tex
+\input{exercises/_common_header.tex}
+\Newassociation{solution}{Solution}{week_2_solution}
+\newif\ifDisplaySolutions\DisplaySolutionstrue%
+
+\begin{document}
+\title{Quantitative Macroeconomics\\~\\Winter 2024/25\\~\\Week 2}
+\author{Willi Mutschler\\willi@mutschler.eu}
+\date{Version: 1.0\\Latest version available on: \href{https://github.com/wmutschl/Quantitative-Macroeconomics/releases/latest/download/week_2.pdf}{GitHub}}
+\maketitle\thispagestyle{empty}
+
+\newpage
+\Opensolutionfile{week_2_solution}[week_2_solution]
+\tableofcontents\thispagestyle{empty}\newpage
+
+\setcounter{page}{1}
+\input{exercises/visualizing_time_series_data.tex}\newpage
+\input{exercises/definition_frequencies_time_series_data.tex}\newpage
+\input{exercises/fundamental_concepts_univariate_time_series.tex}\newpage
+\printbibliography%
+\newpage
+
+\Closesolutionfile{week_2_solution}
+\ifDisplaySolutions%
+\newpage
+\appendix
+\section{Solutions}
+\input{week_2_solution}
+\fi
+\end{document}
\ No newline at end of file