Will Cochrane-Orcutt process remedy heteroskedasticity? Using GRETL

I tried searching for this in the forums but cant seem to find anything. I'm probably just wording it wrong.

I'm working on a research project for school and have pushed most of the way through it. I'm just unclear on how to remedy the issue of heteroskedasticity in my data.

I'm looking for what effect the price of gas has on the air quality index. It's time series data taken monthly.

Most of the variables were non-stationary when I ran the ADF test in GRETL. I solved that by taking first differences of the variables in question. I checked for multicollinearity using VIF and I'm in good shape. I ran a White's test for heteroskedasticity and it shows that it is present. I was taught to run Newey West robust errors to solve that. The problem is that I have significant serial correlation in most of my variables. From readings I gather that Newey West doesnt work on lagged (and I'm assuming first differenced) dependent variables. When estimated the equation with Newey West it didnt change anything and my Durbin Watson for the equation was still in range of positive serial correlation.

So here's my question: In GRETL, you can estimate the equation as a time series using AR(1) with the option of using the Cochrane Orcutt. Does that resolve the issue of Heteroskedasticity? If not, how would you model that?

I apologize if this seems disorganized I've been working on this for weeks with a newborn baby wreaking havoc in the background. I think my head is about to explode. Thank you in advance for any help you can offer.


TS Contributor
You could try to model the error terms as a GARCH model. I've never heard of Cochrane Orcutt, but it seem to be a special case of GARCH, namely GARCH(1,0) if I'm not mistaken. So yes, Cochrane Orcutt may remedy your problem; but I would suggest you try to model your error terms as a GARCH(1,1) process.