Unit Root Tests with EViews (Time Series)

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.

Null Hypothesis: GDP has a unit root
Exogenous: Constant,Linear Trend
Lag Length: 1 (Automatic - based on SIC, maxlag=11)
			t-Statistic	Prob.*
Augmented Dickey-Fuller test statistic			-2.215287	0.4749
Test critical values:	1% level		-4.068290
	5% level		-3.462912
	10% level		-3.157836
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(GDP)
Method: Least Squares
Date: 08/23/16   Time: 11:35
Sample (adjusted): 1971Q3 1992Q4
Included observations: 86 after adjustments
Variable	Coefficient	Std. Error	t-Statistic	Prob.
GDP(-1)	-0.078661	0.035508	-2.215287	0.0295
D(GDP(-1))	0.355794	0.102691	3.464708	0.0008
C	234.9729	98.58764	2.383391	0.0195
@TREND("1971Q1")	1.892199	0.879168	2.152260	0.0343
R-squared	0.152615	Mean dependent var		23.34535
Adjusted R-squared	0.121613	S.D. dependent var		35.93794
S.E. of regression	33.68187	Akaike info criterion		9.917191
Sum squared resid	93026.38	Schwarz criterion		10.03135
Log likelihood	-422.4392	Hannan-Quinn criter.		9.963134
F-statistic	4.922762	Durbin-Watson stat		2.085875
Prob(F-statistic)	0.003406

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

Null Hypothesis: D(GDP) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=11)
			t-Statistic	Prob.*
Augmented Dickey-Fuller test statistic			-6.630339	0.0000
Test critical values:	1% level		-3.508326
	5% level		-2.895512
	10% level		-2.584952
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(GDP,2)
Method: Least Squares
Date: 08/23/16   Time: 12:17
Sample (adjusted): 1971Q3 1992Q4
Included observations: 86 after adjustments
Variable	Coefficient	Std. Error	t-Statistic	Prob.
D(GDP(-1))	-0.682762	0.102975	-6.630339	0.0000
C	16.00498	4.396717	3.640211	0.0005
R-squared	0.343552	Mean dependent var		0.206977
Adjusted R-squared	0.335737	S.D. dependent var		42.04441
S.E. of regression	34.26717	Akaike info criterion		9.929234
Sum squared resid	98636.06	Schwarz criterion		9.986311
Log likelihood	-424.9570	Hannan-Quinn criter.		9.952205
F-statistic	43.96140	Durbin-Watson stat		2.034425
Prob(F-statistic)	0.000000

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

Null Hypothesis: GDP has a unit root
Exogenous: Constant, Linear Trend
Bandwidth: 4 (Newey-West automatic) using Bartlett kernel
			Adj. t-Stat	Prob.*
Phillips-Perron test statistic			-2.197109	0.4849
Test critical values:	1% level		-4.066981
	5% level		-3.462292
	10% level		-3.157475
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction)				1237.491
HAC corrected variance (Bartlett kernel)				2312.771

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

Null Hypothesis: D(GDP) has a unit root
Exogenous: Constant
Bandwidth: 1 (Newey-West automatic) using Bartlett kernel
			Adj. t-Stat	Prob.*
Phillips-Perron test statistic			-6.607376	0.0000
Test critical values:	1% level		-3.508326
	5% level		-2.895512
	10% level		-2.584952
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction)				1146.931
HAC corrected variance (Bartlett kernel)				1121.949

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.