We have discussed how to perform the
unit root test, namely ADF test , PP test and also DF-GLS test
to test whether our time series data is stationary or not. Given the data, we
conduct each test with the Stata package.
In this section, I would like to
share how we conduct for each test of unit root (like we have done before) with
the EViews package. I don’t want to discuss again some theoretical background
about the test and you can refer again for each test at here, here
and here.
To perfom the test, we will use the
same data when we perform unit root test with Stata , Macro_Eviews, but
the data is already in EViews format (*.wf1) and not (*.dta).
Supposed we used ADF test with constant and trend for
gdp variables;
\(\Delta {{Y}_{t}}={{\beta
}_{1}}+{{\beta }_{2}}t+\delta {{Y}_{t-1}}+\sum\limits_{i=1}^{m}{\Delta
{{Y}_{t-i}}+{{\varepsilon }_{t}}}\) (1)
Before we run the ADF test, lets
take a look the graph for each series;
Select the icon gdp,pce, pdi
and the click right mouse and select Open\As Group
and then, click View\Graph…
Select;
Graph type : Basic graph
Spesific : Line & Symbol
Do the same procedure for variables div
and profit.
ADF TEST
Now, lets we perfom the ADF test
first. To do this, click the icon gdp, and then click Views\Unit Root
Test…
and then selects;
Test type: Augmented
Dickey-Fuller.
Test for unit root in : Level
Include in test equation : Trend
and intercept
Lag length : Automatic Selection
– Schwarz Info Criterion. Max lags = 11
and then, click OK.
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Null Hypothesis: GDP has a unit root
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Exogenous: Constant,Linear Trend
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Lag Length: 1 (Automatic - based on SIC, maxlag=11)
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t-Statistic
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Prob.*
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Augmented Dickey-Fuller test statistic
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-2.215287
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0.4749
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Test critical values:
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1% level
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-4.068290
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5% level
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-3.462912
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10% level
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-3.157836
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*MacKinnon (1996) one-sided p-values.
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Augmented Dickey-Fuller Test Equation
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Dependent Variable: D(GDP)
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Method: Least Squares
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Date: 08/23/16 Time:
11:35
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Sample (adjusted): 1971Q3 1992Q4
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Included observations: 86 after adjustments
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Variable
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Coefficient
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Std. Error
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t-Statistic
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Prob.
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GDP(-1)
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-0.078661
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0.035508
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-2.215287
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0.0295
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D(GDP(-1))
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0.355794
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0.102691
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3.464708
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0.0008
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C
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234.9729
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98.58764
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2.383391
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0.0195
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@TREND("1971Q1")
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1.892199
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0.879168
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2.152260
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0.0343
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R-squared
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0.152615
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Mean
dependent var
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23.34535
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Adjusted R-squared
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0.121613
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S.D.
dependent var
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35.93794
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S.E. of regression
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33.68187
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Akaike
info criterion
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9.917191
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Sum squared resid
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93026.38
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Schwarz
criterion
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10.03135
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Log likelihood
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-422.4392
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Hannan-Quinn
criter.
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9.963134
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F-statistic
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4.922762
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Durbin-Watson
stat
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2.085875
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Prob(F-statistic)
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0.003406
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The
results for ADF test show that the \({{\tau }_{s}}=-2.215\), and if we choose
significant level \(\alpha =0.05\), the \({{\tau
}_{c}}=-3.462\).
The
decision is we fail to reject the null hypothesis for unit root.
That
means the series of gdp (in level)
is contained unit root processes and thus it’s nonstationary.
It’s
clear that all series is nonstationary or contained unit root in level form and
we need the time series to be stationary.
The
non-stationary series usually can be eliminated when we difference the series.
That
means, we need to generate the new series
in first difference form.
To
do this, click Genr
Inside the box Enter equation, type
the new variables and the functions (first difference)
ddiv=d(div)
dgpd=d(gdp)
dpce=d(pce)
dpdi=d(pdi)
dprofit=d(profit)
Plot the graph same as we do before;
The graph for each series not shown the clear trend.
Mean that we choose to perform the DF test for variable gdp in first difference .
Now, lets we perfom the ADF in first
difference, click the icon gdp, and then click Views\Unit Root Test…
and then selects;
Test type: Augmented
Dickey-Fuller.
Test for unit root in : 1st
difference
Include in test equation : Intercept
Lag length : Automatic Selection
– Schwarz Info Criterion. Max lags = 11
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Null
Hypothesis: D(GDP) has a unit root
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Exogenous:
Constant
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Lag
Length: 0 (Automatic - based on SIC, maxlag=11)
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t-Statistic
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Prob.*
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Augmented
Dickey-Fuller test statistic
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-6.630339
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0.0000
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Test
critical values:
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1% level
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-3.508326
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5% level
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-2.895512
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10% level
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-2.584952
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*MacKinnon
(1996) one-sided p-values.
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Augmented
Dickey-Fuller Test Equation
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Dependent
Variable: D(GDP,2)
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Method:
Least Squares
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Date:
08/23/16 Time: 12:17
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Sample (adjusted):
1971Q3 1992Q4
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Included
observations: 86 after adjustments
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Variable
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Coefficient
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Std.
Error
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t-Statistic
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Prob.
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D(GDP(-1))
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-0.682762
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0.102975
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-6.630339
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0.0000
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C
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16.00498
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4.396717
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3.640211
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0.0005
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R-squared
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0.343552
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Mean dependent var
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0.206977
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Adjusted
R-squared
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0.335737
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S.D. dependent var
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42.04441
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S.E. of
regression
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34.26717
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Akaike info criterion
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9.929234
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Sum
squared resid
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98636.06
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Schwarz criterion
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9.986311
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Log
likelihood
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-424.9570
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Hannan-Quinn criter.
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9.952205
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F-statistic
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43.96140
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Durbin-Watson stat
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2.034425
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Prob(F-statistic)
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0.000000
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The
results for ADF test show that the \({{\tau }_{s}}=-6.30\), and if we choose
significant level \(\alpha =0.05\), the \({{\tau
}_{c}}=-2.895\).
The
decision is we successful reject the null hypothesis for unit root.
That
means the series of gdp in first
difference is stationary.
PP
TEST
For the PP test, click the icon gdp, and then click Views\Unit Root Test…
and then selects;
Test type: Phillips-Perron
Test for unit root in : Level
Include in test equation : Trend
and intercept
Spectral estimation method : Default
Bandwidth : Newey-West Bandwidth
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Null
Hypothesis: GDP has a unit root
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Exogenous:
Constant, Linear Trend
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Bandwidth:
4 (Newey-West automatic) using Bartlett kernel
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Adj. t-Stat
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Prob.*
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Phillips-Perron
test statistic
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-2.197109
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0.4849
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Test
critical values:
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1% level
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-4.066981
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5% level
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-3.462292
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10% level
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-3.157475
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*MacKinnon
(1996) one-sided p-values.
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Residual
variance (no correction)
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1237.491
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HAC
corrected variance (Bartlett kernel)
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2312.771
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The results for PP test show that the \({{\tau }_{s}}=-2.197\), and if we choose significant level \(\alpha =0.05\), the \({{\tau }_{c}}=-3.462\).
The
decision is we fail to reject the null hypothesis for unit root.
That
means the series of gdp (in level)
is contained unit root processes and thus it’s nonstationary.
The results is consistent with the ADF test.
Lets now we test
the gdp in first difference. Click the icon gdp again, and then click Views\Unit Root
Test…
and then selects;
Test type: Phillips-Perron
Test for unit root in : 1st
difference
Include in test equation : Intercept
Spectral estimation method : Default
Bandwidth : Newey-West Bandwidth
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Null
Hypothesis: D(GDP) has a unit root
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Exogenous:
Constant
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Bandwidth:
1 (Newey-West automatic) using Bartlett kernel
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Adj. t-Stat
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Prob.*
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Phillips-Perron
test statistic
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-6.607376
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0.0000
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Test
critical values:
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1% level
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-3.508326
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5% level
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-2.895512
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10% level
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-2.584952
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*MacKinnon
(1996) one-sided p-values.
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Residual
variance (no correction)
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1146.931
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HAC
corrected variance (Bartlett kernel)
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1121.949
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The
results for PP test show that the \({{\tau }_{s}}=-6.07\), and if we choose
significant level \(\alpha =0.05\), the \({{\tau
}_{c}}=-2.895\).
The
decision is we successful reject the null hypothesis for unit root.
That
means the series of gdp in first
difference is stationary.
We
see that the critical value for the ADF and PP test is identical. That means the PP test using the DF table for
their critical value.
