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:
In order to display the interest series (
) together with the other
two series in one panel we changed its scaling by factor 10.
It seems that
and
may be subject to linear trend and/or
exponential growth.
It is clear from this graph that
and
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
is given to
domulti.
Here we choose both transformations for the series
and
.
Since we deal with seasonally adjusted data we use the default differencing
lag of 1.
After performing the transformations with the two menus above we plot the
transformed time series which gives the following graphics:
Note that our sample size reduced to 119 observations after differencing once.
In the last picture the interest rate series is scaled by factor
.
Now it is reasonable to assume mean and variance stationarity of
the
and
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.