ADF, Stationary/Non Stationary Data

[Rose Banda]

Hi everyone.


I was trying to check my data to see if I have stationary or non stationary data. I am using annual data with no gaps and my dataset comprises 6 variables.

I started by running the regression using the command:

reg lco2 lgdp lpopd lpopg lfdi lper

then performed the Durbin-Watson d-statistic using the command

estat dwatson

My Rsquare ( 0.6740) is less than Durbin-Watson d-statistic (0.9382188) indicating that the series is stationary.

However I wanted to confirm this using ADF test. When I ran the ADF test, it showed that 2 of my variables where non stationary at all critical levels while 3 were not. I then created new variables at the first difference based on already transformed data (i.e. transformed to the logarithmic form) and performed the ADF again.

However, I noticed that some of my data points for the first differenced var had some negative values. see a short extract of the lco2 var which only shows one value as positive (12 points total with positive values and the rest negative for dco2 if you look at the entire timeline)

lco2	dco2
.2551924
.2537923	-.0087013
.2412684	-.0017993
.2140184	-.0014001
.1825199	-.0125239
.2224333	-.0272499
.2106815	-.0314985
.1640534	.0399134
.1612443	-.0117518
.1641062	-.0466281
.1662048	-.002809

The results of the ADF on the differenced var were also mixed. For the dependent var, the t stat in its absolute form was larger than the critical vales at all points, for one of my independent var, it is only larger at 5 and 10% critical value point and for another independent variable, the absolute value is not larger than any critical values at any points. for 3 of my control variables the absolute values of t sata is larger than all critical values at all point.

I want to run either a VAR, VECM or ARDL at the end.

1. How do I deal with the issue of these mixed results from the ADF and with the negative values in the differenced var?
2. should I just forgo the ADF given the result of the D.Wastson in the first regression result. When I ran regression before difference, 4/5 independent var showed to be statistically significant and have an effect on co2. however with the differenced vars, non are significant

Thank you all

Rose

[Justin Niakamal]

I want to run either a VAR, VECM or ARDL at the end.

These have different purposes. VARs/VECMs are useful for things such as impulse response analysis, Granger causality tests, and forecast-error variance decompositions.

2. should I just forgo the ADF given the result of the D.Wastson in the first regression result. When I ran regression before difference, 4/5 independent var showed to be statistically significant and have an effect on co2. however with the differenced vars, non are significant

Is your dependent variable I~(1)? If so, I would look into ardl (from SSC). Read about it here.

[Rose Banda]

Thanks Justin

These are my actual results after ADF test

VAR	At Level	First difference
lco2	non stationary	stationary
lgdp	non stationary	non stationary
lpopd	stationary	stationary
lpops	stationary	stationary
lfdi	non stationary	stationary

How do I proceed with this. I can't run the VAR cause this can only be run if variables are integrated at order 1. I also believe that I can't run the ARDL since I have a variable (gdp) not intergrated at 0 or 1.

Thanks.

[Justin Niakamal]

I can't run the VAR cause this can only be run if variables are integrated at order 1

I'm not sure where you've heard this. Most texts suggest you transform all series until they're I~(0) and then run a VAR.

I also believe that I can't run the ARDL since I have a variable (gdp) not intergrated at 0 or 1.

I would post your data here using dataex -- which country has GDP I~(2)? Is this real or nominal?

[Rose Banda]

Thanks Justin, I originally used GDP per capita (current US$). I have now tested the ADF on other types of GDP. For annual GDP per capita, I find that it is non stationary at level and stationary at first difference.

This now means that I have 3 variables that were non stationary at level and then stationary at first different and remaining variables were stationary at level and also at first difference.

In this case (using annual GDP per capita), the best model for me to use is ARDL right?

[Justin Niakamal]

In this case (using annual GDP per capita), the best model for me to use is ARDL right?

Yes because your dependent variable is I~(1) and no variables are I~(2). It doesn't matter if your independent variables are I~(1) or I~(0) (or borderline). I would go with ardl and check for long-run relationships, etc. An excellent starting point is Sebastian Kripfganz's presentation (see here). There is also a user-written package for visualizing the effects of autoregressive distributed lag models called dynardl. I haven't used it and only recently discovered it but you can check it out here.

Hope this helps

[Rose Banda]

Thanks ALOT!!!