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Very new to all of this, and I can't say I'm feeling comfortable. I have a couple questions, which I'm sure some of you know the answer to.

So my data series' are non-stationary. I did the dickey-fuller test and a couple of the variables are stationary at first difference, and a couple others are only stationary at second difference.

To make sure I'm doing this right, take one of my variables (enrollment). To get the second difference for this, I would enter the command "denrollment=d(enrollment, 2)" and at first difference: "denrollment=d(enrollment)"...correct?

Also, after doing this, when going inside the data, it's completely changed. What is this doing to my data exactly? I just know that it is fixing the stationary issue.

Is taking the second difference of my data effective or should I be avoiding this?

Last question - using the HAC(Newey-West) covariance method fixes autocorrelation and heteroskedacity?

Thanks to anybody who can be of assistance, cheers.

1. I think you are right for the difference command.
2. Of course, it will be changed. You just removed the stochastic trend from your data (enrollment). This means your data mean and variance is not time varying (not constant). Difference command explanation: d(enrollment) = enrollment - enrollment(-1)
3. You should be very careful for the difference of data. First test structural break
Second it depends on your research project. For example, you do VAR then you don't need difference data. It may wipe out long term relationship between data series.
4. For last question, I think you are right.

1. I think you are right for the difference command.
3. You should be very careful for the difference of data. First test structural break
Second it depends on your research project. For example, you do VAR then you don't need difference data. It may wipe out long term relationship between data series.

What do you mean when you say test structural break?

Thanks for the response.

For example, Perron (1989) showed that failure to allow for an existing break leads to a bias that reduces the ability to reject a false unit root null hypothesis.

HAC does not fix anything. It just corrects the covariance matrix so as to take into account the heteroscedasticity in your data. It changes the standard errors (hence the confidence intervals) of parameter estimates, not their means.

There is nothing wrong with taking the second difference from a theoretical point of view. However, it would be better if the resulting series actually has a practical meaning or relates to an existing concept. For instance, first (log) difference of a price index corresponds to inflation. If it still does not become stationary, then you can try taking the second difference and label it as "disinflation/reflation", for instance.

Yes, there are lots of things that can lead to nonstationarity in the series. You should always check/test for outliers, structural breaks, heteroscedasticty etc. before moving on to higher order differencing.