[Gretl-users] Re: FGLS/WLS estimation
Am 25.06.2019 um 01:55 schrieb javier.garcia(a)ehu.es:
Some comments:
1) I agree with you, there are many ways to check whether the
residuals are white noise, but the Breusch-Godfrey test (the one our students usually
employ in an introductory course of econometrics) cannot be run this way. Again, they
should make this "by hand".
Hi,
we're talking about ARMA models, which are not regressions. Even a model
with assumed AR(1) _errors_ is quite different from an AR(1) model of
the endogenous variable (where a lag of that variable is used). Again,
not a regression.
So you cannot run the auxiliary regression needed for the LM test,
because you cannot throw in the original regressors, because the AR and
MA terms of the errors are not observable variables. Please show us any
software that claims to perform this test in this situation.
You say you do something "by hand" - I can only speculate that you save
the residuals, and then regress them on (a constant and) their own lags,
and look at T*R2. This is probably good enough as a pragmatic
workaround, but it ignores that the residuals are estimated objects and
I wouldn't call it the Breusch-Godfrey test.
2) When FGLS estimator is applied to deal with the autocorrelation
problem (for example using Cochrane-Orcutt), statistics based on the rho-differenced data
give the mean (and the standard deviation) of the original dependent variable, whereas all
the other statistics are based on the weighted data. Why this difference?
I'll pass on this one.
3) With Cochrane-Orcutt $uhat gives the GLS residuals, but with WLS
the residuals are the originals (not the weighted ones). Again, why this difference? In
essence the procedure is the same (GLS/FGLS).
I agree, this sounds incoherent (as I've said before), unless I'm
missing something right now. So I repeat: "perhaps it would be an idea
to offer both. " (original and transformed)
cheers
sven