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ANALYSING TIME SERIES DATA USING EVIEWS: A CASE FOR SINGLE
EQUATION MODEL.
January 20th, 2018/ Kuranga Abdulazeez/ Gifted Hands Associate/
09038520999
A single equation model is a model such that there is only one
direction of causality
between the dependent and the independent variable. This means
that in a single
equation model, the independent variable affects the dependent
variable but
the dependent variable does not in any way have any effect on
the
independent variable.
Time series data have some kind of characteristics which make
them to be unique, of
which their ability to have a time trend as well as having mean
and variance that are
not constant. Therefore, in modelling time series data, there
are certain possible
scenarios which one faces:
1. Series have no time trend and are stationary. This means that
the time
series data is not moving at all i.e increasing or decreasing,
but the mean and
variance are constant over time. This is a very rare case
because it is almost
impossible to have variables that are not moving over time and
yet the mean or
variance will be constant.
2. Series are trending but stationary. In this case, it means
the data are either
moving upward or downward (which can also be a random movement),
yet the
mean and variance are constant. This is also a very rare
case.
3. Series are trending, not stationary and not co-integrated. In
this case, it
means that the data is either increasing or decreasing overtime,
the mean and
variance are not constant. They also do not have relationship
either in the long
run or in the short run. This is a possible scenario because it
is expected that
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once a variable is trending, then the mean and the variance will
not be constant
over time.
4. However, the very possible case to encounter for single
equation model is when
the series are trending and not stationary but they are co
integrated.
This means that apart from the data following the normal way of
trending and
not having constant mean and variance, they also have long run
relationships.
STEP BY STEP METHOD OF ANALYSIS
1. Import the excel file into Eviews. Click on finish while
making sure that the data
is well arranged.
Figure 1
When you click on the ‘finish’ button, it will bring the image
below:
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Figure 2
2. Double click on each variable to see that the data is the
same with the one
in your excel file. To view the trend, click on the variable you
want: VIEW ----
GRAPH.
Figure 3
When you click on ‘Graph’, the dialogue box below will appear,
and you should
make sure to click ‘OK’ after you have chosen the kind of graph
you want:
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Figure 4
You can also check the graphical illustration in Excel by
highlighting the data on
the variable you want and press ALT+F1.
To view if it has unit root, that is, if the mean and variance
are non-stationary:
VIEW --- UNIT ROOT. That is, you click on view (as displayed in
figure 3), and
then go down to pick ‘unit root test’ as an option. Here, a
dialogue box will appear
as shown below: Figure 5
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First of all test at level while including trend in your
equation. In the result, check
the P-value. If it is greater than any of the chosen level of
significant, you go back
to test at first difference. If it is also not significant. Then
you will have to create
a log of that variable (Another situation in which you can also
log is
when the variable values are probably huge or you want to change
the
variables to percentage). To log in eviews: genr l(variable)=
log
(variable). Then click on the enter button. Then you will go
back testing the
variable for unit root normally. For example, in the data I
used, GDPI was not
significant at level and first difference, so I logged it as
shown below:
Figure 6
From figure 6 above, it can be seen that after entering the
command for logging a
variable, another variable ‘lgdpi’ was created. And by testing
for the unit root of
this, it was seen to be significant at first difference as seen
in figure 7 below:
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Figure 7
So the number of times you difference your variable to let it be
stationary will
determine how you will call the variable. Therefore, if you test
for the unit
root at level and it becomes stationary, it will be referred to
as I(0). If
differenced at first difference, then it will be referred to as
I(1) and so
on. Also, if your variable becomes stationary when you log it,
then it is
the log of that variable that will be included in your model and
when
you are interpreting, you interpret in percentages.
3. If after testing for the unit root and the variables are all
I(0) series, then you run
normal OLS with de-trending.
4. If after testing for unit root and all the variables are I(1)
series, then you run a
co integrating test using Engel and granger to determine the
long run
relationship among the variables. To run Engel-Granger test:
first highlight the
variables (while letting the dependent variable come first),
then right click and
open as a group as shown in figure 8 below:
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Figure 8
Click on View, go down to where ‘co integrating test’ is. Click
on it and then click on
‘single equation co integration test’ as shown in figure 9
below:
Figure 9
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NOTE: This is where most researchers make mistakes when
analysing
time series data. You only use ‘Johansen system Co-integration
test’ for
systems of equation and not for single equation models. The
single
equation co-integration test is used for single equation models.
Therefore,
if your model is such that only the independent variables have
effect on
the dependent variable while the dependent variable does not
affect the
independent variable both in theory and common sense, then the
single
equation co integration test is what you should use as your test
for
relationship among the variables.
Continuing from figure 9, once you click on the Single equation
co integration test, a
dialogue box will appear as in figure 10 below:
Figure 10
Change the ‘constant trend’ to ‘linear trend’ and then click on
OK (that is, VIEW- CO
INTEGRATING TEST- SINGLE EQUATION CO INTEGRATING TEST- OK.
The decision rule is that if at least one of the variables is
significant, it indicates that
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there is co integration among the variables. Therefore, you
either run A Fully Modified
Ordinary Least Square (FMOLS) or Short run Error Correction
Model (ECM).
To run FMOLS, highlight the variables (while letting the
dependent variable
come first), right click and open as an equation. A dialogue box
will appear,
change the option to ‘co integrating regression’ (as shown in
figure 11) after which
another dialogue will appear as shown in figure 12.
Figure 11
Figure 12
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Change the constant (level) to linear trend because we are
adjusting for time trend.
Then click on OK. The output will be shown as the one in figure
13 below, and you can
then interpret accordingly.
Figure 13
5. If after testing for unit root and some of the variables are
I(0) while others are
I(1), the best method of analysis is the bounds test, even
though FMOLS is
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also good. So any of the method can be determined by your
supervisor or what
you like.
PERFORMING BOUNDS TEST
1. Highlight the variables. Make sure your dependent variable
comes first
2. Open as equation and change the option to the last one which
is Auto-
Regressive Distributive Lag Models (ARDL) and then click OK.
3. Another dialogue box will open. Adjust the lag to suit your
taste and then click
OK.
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4. From the result that will be shown, click on VIEW. Then
COEFFICIENT
DIAGNOSTIC and also BOUNDS TEST (VIEW- COEFFICIENT
DIAGNOSTIC- BOUNDS TEST)
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5. If F statistic is greater than the upper and lower bound,
then there is co
integration. Next thing to do here is just to run your final
analysis which will be
to either run FMOLS or co integration long run as well as short
run coefficient.
To do this, click on VIEW- COEFFICIENT DIAGNOSTIC- CO
INTEGRATION AND LONG RUN FORM.
Then you results will show like the figure below and interpret
your results accordingly.
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6. If F statistic is less than the upper and lower bound, then
there is no co-
integration. What to do here is to click on ESTIMATE. A dialogue
box will
appear as shown below:
Add D in front of each of the variables and bracket each of them
(do not bracket the D)
as shown below: Interpret your result.
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7. If F statistic is in between (less than the upper bound and
greater
than the lower bound), then it is in conclusive. What you will
do in this
case is to go back to adjust your lag until the F statistic is
either greater than the
upper and lower bound or less than the upper and lower bound.
Then, apply
the appropriate method of analysis.
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REFERENCES
Kilishi A.A (2015). Modeling With Time Series: Issues and Common
Errors.
Department of Economics, University of Ilorin, Ilorin, Kwara
State.
Gujarati N.D and Porter D.C (2009). Basic Econometrics, New
York: McGraw Hill.