Re: [Gretl-users] issues with the DF/EG tests
On Tue, 8 May 2012, Sven Schreiber wrote:
ah ok, I think I now understand the second part. However, that's
an area
where one has to be very careful.
For example, if you have two variables with trends/drifts, regressing
one on the other with only a constant (and no trend term) you are
actually running a co-trending regression, not a cointegration
regression. There's a good chance that the estimator and the test in
such cases then doesn't have the properties you expect.
I see your point that you want to have more control over the options in
the Engle-Granger test, and maybe you're right. But what gretl does
seems quite reasonable so far. If you want to do the dangerous stuff
described above, of course you can do it manually by running the right
regressions, and some people out there on this mailing list would argue
that that's a good thing...
Count me as one such! The Engle-Granger test regressions are
not rocket science and if one wants to do something
non-standard that's fine, but there's little point in larding
the "coint" command with additional options.
Depending on which version of gretl Daniel and his students
are using, they might note that the printout of the final
stage of the Engle-Granger test was fixed in gretl 1.9.8 (the
numbers were OK but the string representing the model
estimated was not exact). Also a --verbose option was added,
which enables you to see exactly what's going on.
Allin Cottrell
context:
Am 08.05.2012 19:37, schrieb Daniel Ventosa S.:
> Hi,
> Many thanks. So, for the DF tests on the original variables, the
> Engle-Granger uses the smallest available sample size. I understand the
> argument and it seems to be the strongest one. However, considering that
> the ultimate goal is to identify unit roots in the variables, it also
> could be argued that using all the available information is better than
> just using a part of it; It's true, the tests will not be strictly
> comparable, but the goal is not to compare them; what the practitioner
> should do is to ensure that the ADF tests correctly rejects/does not
> reject the null. Anyway, that's not the main issue: suppose you use the
> Engle-Granger test and include constant term and trend for the ADF tests
> on the variables. It turns out that the specification of the
> cointegration equation includes exactly the same deterministic
> components. It's quite easy to imagine a number of data-generating
> processes for, say, x_t and y_t, that do not fit the model used by
> GRETL: x_{t}=m+x_{t-1}+u_{t} (unit root with drift, i.e. deterministic
> trend); y_{t}=a+b*x_{t}+w_{t} with w_t~I(0). To test for the unit root
> in x, you need to include constant term and trend; the same goes for y,
> since it includes x. Nevertheless, the cointegration equation does not
> have trend. Maybe I am missing something really obvious (and I'm sorry
> if that's the case), but I think you should be able to decide, as a
> separate option, what deterministic elements should be included in the
> ADF tests and in the cointegration equation.