Dickey Fuller Verses Phillips Perron Unit Root Tests : A Review

In this simple tutorial, we demonstrate the basic review of Dickey Fuller Verses Phillips Perron Unit Root Tests. The comparison is based on the null hypothesis formulation, critical values computation and regression specification to test the null of unit root in the series.

We can see from the file file details for Dickey Fuller Unit Root that

it performs the augmented Dickey-Fuller test that a variable follows a unit-root process. The null hypothesis is that the variable contains a unit root, and the alternative is that the variable was generated by a stationary process. You may optionally exclude the constant, include a trend term, and include lagged values of the difference of the variable in the regression (Stata Help File for Dickey Fuller Unit Root test).

while the details in the Stata help file or Phillips-Perron unit root tests are:

Phillips Perron Unit Root Test provided evidence on that a variable has a unit root. The null hypothesis is that the variable contains a unit root, and the alternative is that the variable was generated by a stationary process. Phillips Perron Unit Root Test uses Newey-West standard errors to account for serial correlation, whereas the augmented Dickey-Fuller test implemented in Dickey Fuller Unit Root uses additional lags of the first-difference variable (Stata Help File for Phillips Perron Unit Root Test).

This gives us the basic observation on Dickey Fuller Verses Phillips Perron Unit Root Tests that the null hypothesis of the both is same that the variable is unit root against the alternative of no unit root. Also, we can see that the regression specification is different because Dickey Fuller Unit Root adjusted the regression model through addition of additional lags in the equation and Phillips Perron Unit Root Test uses Newey-White adjustment for the residuals to cover for serial correlation.

The following regression specification is used in Dickey Fuller Unit Root test in Stata:

Dickey Fuller Verses Phillips Perron Unit Root Tests 1

and the null hypothesis that Y is unit root when β=0 is rejected.

Now, we can see the regression model to test unit root in Phillips Perron unit root test as:

Dickey Fuller Verses Phillips Perron Unit Root Tests 2

Where the null hypothesis of unit root is tested based on ρ=1 is rejected. Note, the above equation is estimated with the Newey–West (1987) heteroskedasticity- and autocorrelation-consistent covariance matrix estimator. Also, Phillips and Perron (1988) proposed two alternative statistics. Phillips and Perron’s test statistics can be viewed as Dickey–Fuller statistics that have been made robust to serial correlation by using (Stata Help File for Phillips Perron unit root test).

These differences in the regression specification can easily be found in the two regression results from Stata to compare Dickey Fuller Verses Phillips Perron Unit Root Tests. The first image is showing results DFULLER command as:

Dickey Fuller Verses Phillips Perron Unit Root Tests 3

While the results output from PPERRON command is:

Dickey Fuller Verses Phillips Perron Unit Root Tests 4

Where we can easily see the difference between the two tests. PPERRON does not add the lags as we see in DFULLER commands output because Dickey Fuller Verses Phillips Perron Unit Root Tests differ in the nature of controlling for Standard Errors and Serial Correlation in the regression model and basic null hypothesis of the two tests remains the same.

Note, Dickey Fuller Verses Phillips Perron Unit Root Tests are actually based on these simple specifications:

Dickey Fuller Verses Phillips Perron Unit Root Tests 5

I am sure this basic tutorial on Dickey Fuller Verses Phillips Perron Unit Root Tests would help you determine the true nature of the given tests and in selection of unit root nature of the time series data through application of these approaches in Stata.

To learn more, I recommend our online courses in Applied Econometrics Research here.

Phillips-Ouliaris Cointegration Test

In this short tutorial in Eviews, we would explain the basic steps of conduting Phillips-Ouliaris Cointegration Test. To run Phillips-Ouliaris Cointegration Test in Eviews, we will need to ender the data as dated frequency and panel structure. Theoretically, the Phillips-Ouliaris Cointegration Test can found well explained in P. C. B. Phillips and S. Ouliaris (1990): Asymptotic Properties of Residual Based Tests for Cointegration. Econometrica 58, 165–193 which can be downloaded here.

Phillips-Ouliaris Cointegration Test

To run Phillips-Ouliaris Cointegration Test in Eviews, open Eviews and follow the steps below:

The following video tutorial explains the above steps to help replication be more convenient. If you would like to learn more about Applied Econometrics Research using Eviews, check our private and instructor led courses here.

ARDL and Unit Root Testing using Eviews

ARDL Cointegration using Eviews 9

To estimate ARDL using Eviews 9 on Time Series Data, first open the data file/workfile, Click on your DV, press control key on keyboard, now left click to select all your IVs one by one, once selected then right click on any selected variables and open these as Equations. Once you get the Methods window in Eviews, go the methodology selection from Estimation Setting near to bottom, select ARDL from the list and click Okay. Now you cans elect the lags of DV and IV and any other options for the the methods. You can click on the OK button to get your estimates.

Augmented Dickey Fuller Unit Root Test using Eviews

Augmented Dickey Fuller Unit Root Test using Eviews We can test a time series variable for Unit Root Test following Augmented Dickey Fuller Approach in Eviews following the steps outlined below. First of all open the Eviews workfile or the Excel data in Eviews, then right click on any of the variables we would like to test for unit root based on Augmented Dickey Fuller Approach and click on Open. The series opens in spreadsheet in Eviews. We can click on View in the left upper corner of the new spreadsheet window in Eviews. Then we can click on Unit Root Test in this list that pops down by clicking on View tab. This opens the dialogue box as shown in the inserted screenshot from Eviews itself, we can see that it has mainly four sections. Main section is related to selecting the test type. The Eviews produces unit root test results following 6 methods. We will select the Augmented Dickey Fuller as test type. The we will select either the Level, Difference or Second Difference. Next we can select either to include intercept or both of trend and intercept or none. On the right side of the same window, we can either ask Eviews to use lags automatically or we can insert manually the maximum lags into the model to base our unit root test on. Once we select everything as per our assumed approach to test a series for unit root using Augmented Dickey Fuller Approach, we can click on OK to get the test results.

Phillips Perron Unit Root Test using Eviews

Phillips Perron (PP) Unit Root Test using Eviews We can test a time series variable for Unit Root Test following Phillips Perron (PP) Approach in Eviews following the steps outlined below. First of all open the Eviews workfile or the Excel data in Eviews, then right click on any of the variables we would like to test for unit root based on Phillips Perron (PP) Approach and click on Open. The series opens in spreadsheet in Eviews. We can click on View in the left upper corner of the new spreadsheet window in Eviews. Then we can click on Unit Root Test in this list that pops down by clicking on View tab. This opens the dialogue box as shown in the inserted screenshot from Eviews itself, we can see that it has mainly four sections. Main section is related to selecting the test type. The Eviews produces unit root test results following 6 methods. We will select the Phillips Perron (PP) as test type. The we will select either the Level, Difference or Second Difference. Next we can select either to include intercept or both of trend and intercept or none. On the right side of the same window, we can either ask Eviews to use lags automatically or we can insert manually the maximum lags into the model to base our unit root test on. Once we select everything as per our assumed approach to test a series for unit root using Phillips Perron (PP) Approach, we can click on OK to get the test results.

KPSS Unit Root Test using Eviews

KPSS Unit Root Test using Eviews We can test a time series variable for Unit Root Test following Kwiatkowski-Phillips-Schmidt-Shin Approach in Eviews following the steps outlined below. First of all open the Eviews workfile or the Excel data in Eviews, then right click on any of the variables we would like to test for unit root based on KPSS Approach and click on Open. The series opens in spreadsheet in Eviews. We can click on View in the left upper corner of the new spreadsheet window in Eviews. Then we can click on Unit Root Test in this list that pops down by clicking on View tab. This opens the dialogue box as shown in the inserted screenshot from Eviews itself, we can see that it has mainly four sections. Main section is related to selecting the test type. The Eviews produces unit root test results following 6 methods. We will select the KPSS as test type. The we will select either the Level, Difference or Second Difference. Next we can select either to include intercept or both of trend and intercept or none. On the right side of the same window, we can either ask Eviews to use lags automatically or we can insert manually the maximum lags into the model to base our unit root test on. Once we select everything as per our assumed approach to test a series for unit root using KPSS Approach, we can click on OK to get the test results.

Ng-Perron Unit Root Test using Eviews

We can test a time series variable for Unit Root Test following Ng-Perron Approach in Eviews following the steps outlined below. First of all open the Eviews workfile or the Excel data in Eviews, then right click on any of the variables we would like to test for unit root based on Ng-Perron Approach and click on Open. The series opens in spreadsheet in Eviews. We can click on View in the left upper corner of the new spreadsheet window in Eviews. Then we can click on Unit Root Test in this list that pops down by clicking on View tab. This opens the dialogue box as shown in the inserted screenshot from Eviews itself, we can see that it has mainly four sections. Main section is related to selecting the test type. The Eviews produces unit root test results following 6 methods. We will select the Ng-Perron as test type. The we will select either the Level, Difference or Second Difference. Next we can select either to include intercept or both of trend and intercept or none. On the right side of the same window, we can either ask Eviews to use lags automatically or we can insert manually the maximum lags into the model to base our unit root test on. Once we select everything as per our assumed approach to test a series for unit root using Ng-Perron Approach, we can click on OK to get the test results.