I really hope you could help me with that. I have an exercise in my 'Financial modelling' module and am quite lost to be honest.
Let's explain the situation: I am dealing with the Dow Jones index.
-The first question of this exercise is to test for unit root. I do that using Perron's procedure and the log of the index and find a unit root. So far so good.
-The second question, and that's where I'm not sure, is to identify an ARMA model for the purpose of estimating the series of equity market returns.
The first problem is that I'm not sure if I have to use the Log Dow Jones which contains a unit-root or the return which does not. I think I have read somewhere that you have to use stationary variables to identify an ARMA model so I used the return (log and difference) and not the log. But obviously, the first difference of my log Dow Jones looks exactly like a pure white-noise process.
So when I estimate my ARMA model, I regress with maximum likelihood a pure white noise which is a bit silly I guess. Then I do the overfitting procedure and actually find that for an ARMA (4,4), all my coefficients are significant and the 'white-noise' test of my residuals is perfect.
So I'm tempted to say that my 'white-noise'-like returns can be modelled by an ARMA (4,4) but I feel like I've done something wrong here.
-Can you really estimate stock returns with an ARMA model?
-Does the lecturer actually asked us to identify the ARMA model on the log and not the return of the index? (but it contains a unit-root so don't think you can do it)
-Does the lecturer actually want us to say that it is not possible?
Ok, sorry with all these questions. I really do hope I've been clear. Let me know if you want me to shed light on a certain point.
Thank you in advance for your help.
Have a good evening