17.2 Preliminary Analysis

This section should generally answer the question what model type corresponds best to the given data. Since the task is to fit a full VAR model the consideration is restricted to the question whether the given data set fits well in a full VAR framework. For this we note that the inference we want to make in Sections 17.3 and 17.4 requires data generated by a stable process. Stability implies mean and variance stationarity of the data. These features will be of interest in the following preliminary analysis.


17.2.1 Plotting the Data

It is good practice to start time series investigation by just visual inspection of the data graphs. We can view all time series in one chart or separate charts. Since we deal with multiple time series analysis we choose option one. This gives the following picture:

\includegraphics[scale=0.6]{mts_data_all}
In order to display the interest series ($ I$) together with the other two series in one panel we changed its scaling by factor 10. It seems that $ M$ and $ Y$ may be subject to linear trend and/or exponential growth. It is clear from this graph that $ M$ and $ Y$ have no stationary mean.


17.2.2 Data Transformation

It is common to handle linear trend by differencing the data. Exponential growth can be transformed by applying the natural logarithm. Exactly these two transformations are supported. If both transformations are chosen the logarithmic transformation is automatically performed first.

Further transformations may be performed with XploRe before the data matrix $ x$ is given to 29979 domulti .

Here we choose both transformations for the series $ M$ and $ Y$. Since we deal with seasonally adjusted data we use the default differencing lag of 1.

\includegraphics[scale=0.7]{mts_pre_select}\includegraphics[scale=0.7]{mts_pre_M1}
After performing the transformations with the two menus above we plot the transformed time series which gives the following graphics:
\includegraphics[scale=0.6]{mts_data_all_trans}
Note that our sample size reduced to 119 observations after differencing once. In the last picture the interest rate series is scaled by factor $ 10^{-2}$.

Now it is reasonable to assume mean and variance stationarity of the $ M$ and $ Y$ series. However, at the beginning of both series we still observe a period of high fluctuations compared with the end. We might keep this feature in mind for later steps of the analysis.