3:12 p.m.
Hello everybody;
I would like to make a suggestion regarding the FGLS/WLS estimator implementation in
Gretl.
When we have a model where the errors present autocorrelation (for example, an AR(1)
process), and we try to get the estimated model this way: Model->Time Series->AR
errors (GLS) -> AR(1), some post-estimation tests/results… are disabled. In particular,
no autocorrelation and/or heteroskedasticity tests can be implemented
(Tests->Heteroskedasticity or Tests->Autocorrelation). My question is: why does this
happen? I think that it would be very useful if these options were active. Otherwise,
after running FGLS there is no possibility to check whether the autocorrelation has been
“corrected”, unless we run the regressions "by hand".
Something similar happens with WLS estimator for the case in which errors show
heteroskedasticity. Furthermore, I think that in this case the Total Sum of Squares (TSS)
based on the weighted data is not properly calculated, because if we run an OLS regression
on the weighted variables all the statistics depending on the TSS (R-squared, Adjusted
R-squared, F value and its p-value…) are different (however, the sum of the squared
residuals, the S.E. of the regression, etc. are right). I suspect that Gretl is mixing
the original dependent variable and the weighted results. Why? Because 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.
Finally, in the WLS estimator option the residuals are the originals, and not the weighted
ones. This should be also changed (with the FGLS estimator this does not happen, being the
residuals the weighted ones).
Best
Javi
5:19 p.m.
Am 18.06.2019 um 17:12 schrieb javier.garcia(a)ehu.es:
Hello everybody;
Hi Javier,
I would like to make a suggestion regarding the FGLS/WLS estimator
implementation in Gretl.
When we have a model where the errors present autocorrelation (for example, an AR(1)
process), and we try to get the estimated model this way: Model->Time Series->AR
errors (GLS) -> AR(1), some post-estimation tests/results… are disabled. In particular,
no autocorrelation and/or heteroskedasticity tests can be implemented
(Tests->Heteroskedasticity or Tests->Autocorrelation).
1) heterosk.: in a time-series context you typically would test for the
ARCH-variant, and that is available.
2) autocorrelation: What you're saying sounds natural at first, but
guess what other software are saying when you ask for such a diagnostic
test after AR-estimation: "Not available with this estimation method
(ARMA ML)." (This is from Eviews 10.) You do get the residual
correlogram and the Q-stats.
Something similar happens with WLS estimator for the case in which
errors show heteroskedasticity. Furthermore, I think that in this case the Total Sum of
Squares (TSS) based on the weighted data is not properly calculated, because if we run an
OLS regression on the weighted variables all the statistics depending on the TSS
(R-squared, Adjusted R-squared, F value and its p-value…) are different (however, the sum
of the squared residuals, the S.E. of the regression, etc. are right). I suspect that
Gretl is mixing the original dependent variable and the weighted results.
Here it would help if you could give a concrete (but ideally very
simple) example, so that we know which numbers you're talking about, and
what you want them to be. (And BTW, have you read command reference for
'wls'?)
Finally, in the WLS estimator option the residuals are the originals,
and not the weighted ones. This should be also changed (with the FGLS estimator this does
not happen, being the residuals the weighted ones).
Not sure I agree, but what do you mean with "the residuals"? Which
object grabbed from which menu or accessor? But in any case, if I view
WLS just as a certain way to get good estimators, I'm still interested
in the original equation, with the original error terms.
thanks
sven
>
> Best
> Javi
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11:08 p.m.
Hello, Sven:
1) heterosk.: in a time-series context you typically would test for the ARCH-variant, and
that is available.
RESPONSE:
Yes, your are right. I was speaking in a broad sense. In a time series context my concern
is mainly the autocorrelation test.
2) autocorrelation: What you're saying sounds natural at first, but guess what other
software are saying when you ask for such a diagnostic test after AR-estimation:
"Not available with this estimation method (ARMA ML)." (This is from Eviews
10.) You do get the residual correlogram and the Q-stats.
RESPONSE:
This is something that we usually do with our students. Once they have estimated the model
by means (for example) of Cochrane-Orcutt, they check whether the autocorrelation has been
correctly "removed". As Gretl does not give that option, in my opinion the
"automatic" FGLS estimation loses atractiveness, as one has to transform the
model and apply OLS "by hand". That is why I suggested activating the
autocorrelation test option.
3) Something similar happens with WLS estimator for the case in which errors show
heteroskedasticity. Furthermore, I think that in this case the Total Sum of Squares (TSS)
based on the weighted data is not properly calculated, because if we run an OLS regression
on the weighted variables all the statistics depending on the TSS (R-squared, Adjusted
R-squared, F value and its p-value…) are different (however, the sum of the squared
residuals, the S.E. of the regression, etc. are right). I suspect that Gretl is mixing the
original dependent variable and the weighted results.
Here it would help if you could give a concrete (but ideally very simple) example, so that
we know which numbers you're talking about, and what you want them to be. (And BTW,
have you read command reference for 'wls'?)
RESPONSE:
Yes, lets use data7-24.gdt
These are the results when we use "pisua" as weight, where "pisua" is
equal to 1/sqft^2
Model 1: WLS, using observations 1-224
Dependent variable: salepric
Variable used as weight: pisua
coefficient std. error t-ratio p-value
----------------------------------------------------------
const −285.205 37.2121 −7.664 5.70e-013 ***
sqft 0.215569 0.00959143 22.48 6.74e-059 ***
age −0.549288 2.28001 −0.2409 0.8098
city 110.780 15.6896 7.061 2.14e-011 ***
Statistics based on the weighted data:
Sum squared resid 0.150742 S.E. of regression 0.026176
R-squared 0.798817 Adjusted R-squared 0.796073
F(3, 220) 291.1769 P-value(F) 2.64e-76
Log-likelihood 500.1866 Akaike criterion −992.3732
Schwarz criterion −978.7266 Hannan-Quinn −986.8648
Statistics based on the original data:
Mean dependent var 642.9294 S.D. dependent var 371.3762
Sum squared resid 4735143 S.E. of regression 146.7085
And these are the results when I build the transformed variables
(variable_n=variable*sqrt(pisua)) and apply OLS in the transformed model:
Model 2: OLS, using observations 1-224
Dependent variable: salepric_n
coefficient std. error t-ratio p-value
----------------------------------------------------------
const_n −285.205 37.2121 −7.664 5.70e-013 ***
sqft_n 0.215569 0.00959143 22.48 6.74e-059 ***
age_n −0.549288 2.28001 −0.2409 0.8098
city_n 110.780 15.6896 7.061 2.14e-011 ***
Mean dependent var 0.153250 S.D. dependent var 0.034928
Sum squared resid 0.150742 S.E. of regression 0.026176
R-squared 0.445905 Adjusted R-squared 0.438349
F(3, 220) 59.01455 P-value(F) 4.97e-28
Log-likelihood 500.1866 Akaike criterion −992.3732
Schwarz criterion −978.7266 Hannan-Quinn −986.8648
AS can be seen, all the statistics depending on the TSS (R-squared, Adjusted R-squared, F
value and its p-value…) are different (however, the sum of the squared residuals, the S.E.
of the regression, etc. are the same)
4) Finally, in the WLS estimator option the residuals are the originals,
and not the weighted ones. This should be also changed (with the FGLS estimator this does
not happen, being the residuals the weighted ones).
Not sure I agree, but what do you mean with "the residuals"? Which object
grabbed from which menu or accessor? But in any case, if I view WLS just as a certain way
to get good estimators, I'm still interested in the original equation, with the
original error terms.
I mean the ones that Gretl saves when in the estimation window I select "Save >
residuals". In the WLS estimation the residuals that Gretl saves are the original
ones, whereas in the FGLS estimation are the transformed ones. It is true that WLS is just
a way to get good estimators, but the propierties of these estimators will depend on the
fact that residuals in the transformed model satisfy the basic assumptions. If there is no
way to check this... how can we be sure about the FGLS estimators' propierties? This
is related to the first comment above.
Thanks a lot for your response.
Yours
Javi
8:17 a.m.
Am 19.06.2019 um 01:08 schrieb javier.garcia(a)ehu.es:
2) autocorrelation: What you're saying sounds natural at first,
but guess what other software are saying when you ask for such a diagnostic test after
AR-estimation: "Not available with this estimation method (ARMA ML)." (This is
from Eviews 10.) You do get the residual correlogram and the Q-stats.
RESPONSE:
This is something that we usually do with our students. Once they have estimated the
model by means (for example) of Cochrane-Orcutt, they check whether the autocorrelation
has been correctly "removed". As Gretl does not give that option, in my opinion
the "automatic" FGLS estimation loses atractiveness, as one has to transform the
model and apply OLS "by hand". That is why I suggested activating the
autocorrelation test option.
What I meant is that there is an underlying econometric reason why that
particular test is de-activated, both in gretl and (for example) in
Eviews. The point is that it is not simply a question of programming
effort to add that. (I am not trying to defend the estimation with AR
error terms, in fact personally I much favor an OLS-based ARDL approach.
But that is not the issue here.)
One might argue that it isn't optimal that the autocorrelation tests are
distributed over two menus (in the model window): one is in 'Tests' (and
that's the one which is deactivated), while the other one is in 'Plots'...
3) ...
RESPONSE:
Yes, lets use data7-24.gdt
I will look at that one later, don't have the time. Or perhaps somebody
else...
4) Finally, in the WLS estimator option the residuals are the
originals,
and not the weighted ones. ...
In the WLS estimation the residuals that Gretl saves are the original ones, whereas in
the FGLS estimation are the transformed ones. It is true that WLS is just a way to get
good estimators, but the propierties of these estimators will depend on the fact that
residuals in the transformed model satisfy the basic assumptions.
If there really is a difference in gretl's behavior in that respect
between WLS and AR, that would indeed not be good I think. I also agree
that it is useful that the transformed residuals could be checked. I'm
not sure right now whether there isn't some other way to get those
(except in the manual way, of course). (Again, cannot check ATM.)
Provided it isn't possible already, perhaps it would be an idea to offer
both.
cheers
sven
3:31 p.m.
Am 19.06.2019 um 01:08 schrieb javier.garcia(a)ehu.es:
3) Furthermore, I think that in this
case the Total Sum of Squares (TSS) based on the weighted data is not
properly calculated, because if we run an OLS regression on the
weighted variables all the statistics depending on the TSS
(R-squared, Adjusted R-squared, F value and its p-value…) are
different (however, the sum of the squared residuals, the S.E. of the
regression, etc. are right). I suspect that Gretl is mixing the
original dependent variable and the weighted results.
Here it would help if you could give a concrete (but ideally very
simple) example, so that we know which numbers you're talking about,
and what you want them to be. (And BTW, have you read command
reference for 'wls'?)
RESPONSE:
Yes, lets use data7-24.gdt
These are the results when we use "pisua" as weight, where "pisua"
is
equal to 1/sqft^2
...
OK, thanks for the example.
AS can be seen, all the statistics depending on the TSS (R-squared,
Adjusted R-squared, F value and its p-value…) are different (however,
the sum of the squared residuals, the S.E. of the regression, etc.
are the same)
I think the arrangement of the statistics after the WLS estimation and
the labeling (weighted/original) is a bit misleading. In fact, it seems
to me that only the SSR and the SE of regr are actually supposed to be
coming from the weighted variant. The R2 (here: 0.7988) is using the
WLS-estimated betas, but then is correctly based on the original data -
because of course you want to compare the fit to the plain OLS on the
original data (which BTW comes out as 0.86 here).
But I agree that the presentation of the results suggests otherwise, and
this should probably be improved. Perhaps we should open a ticket on the
feature request tracker on sourceforge
(https://sourceforge.net/p/gretl/feature-requests/ -- or the bug tracker
would also work, this is a borderline case I'd say).
thanks
sven
3:47 p.m.
On Tue, 18 Jun 2019, javier.garcia(a)ehu.es wrote
(in response to Sven's request for a specific example, and a propos
the auxiliary statistics reported by gretl following weighted least
squares estimation via the "wls" command)
Yes, lets use data7-24.gdt
These are the results when we use "pisua" as weight, where "pisua"
is equal to 1/sqft^2
Model 1: WLS, using observations 1-224
Dependent variable: salepric
Variable used as weight: pisua
coefficient std. error t-ratio p-value
----------------------------------------------------------
const −285.205 37.2121 −7.664 5.70e-013 ***
sqft 0.215569 0.00959143 22.48 6.74e-059 ***
age −0.549288 2.28001 −0.2409 0.8098
city 110.780 15.6896 7.061 2.14e-011 ***
Statistics based on the weighted data:
Sum squared resid 0.150742 S.E. of regression 0.026176
R-squared 0.798817 Adjusted R-squared 0.796073
F(3, 220) 291.1769 P-value(F) 2.64e-76
Log-likelihood 500.1866 Akaike criterion −992.3732
Schwarz criterion −978.7266 Hannan-Quinn −986.8648
Statistics based on the original data:
Mean dependent var 642.9294 S.D. dependent var 371.3762
Sum squared resid 4735143 S.E. of regression 146.7085
And these are the results when I build the transformed variables
(variable_n=variable*sqrt(pisua)) and apply OLS in the transformed
model:
Model 2: OLS, using observations 1-224
Dependent variable: salepric_n
coefficient std. error t-ratio p-value
----------------------------------------------------------
const_n −285.205 37.2121 −7.664 5.70e-013 ***
sqft_n 0.215569 0.00959143 22.48 6.74e-059 ***
age_n −0.549288 2.28001 −0.2409 0.8098
city_n 110.780 15.6896 7.061 2.14e-011 ***
Mean dependent var 0.153250 S.D. dependent var 0.034928
Sum squared resid 0.150742 S.E. of regression 0.026176
R-squared 0.445905 Adjusted R-squared 0.438349
F(3, 220) 59.01455 P-value(F) 4.97e-28
Log-likelihood 500.1866 Akaike criterion −992.3732
Schwarz criterion −978.7266 Hannan-Quinn −986.8648
AS can be seen, all the statistics depending on the TSS (R-squared,
Adjusted R-squared, F value and its p-value…) are different
(however, the sum of the squared residuals, the S.E. of the
regression, etc. are the same)
This is explained in the documentation for the "wls" command. We do
the same thing as R, namely replace the regular TSS with the weighted
TSS, that is, the sum of squared residuals from a regression of the
weighted dependent variable on the weighted constant alone.
Allin
11:39 p.m.
OK, thanks a lot. But... which is the motivation of this approach? Why a
"standard" version of the TSS is not given as the one you obtain if the
regression is run "by hand"?
Best
Javi
7:54 p.m.
On Mon, 24 Jun 2019, javier.garcia(a)ehu.es wrote:
OK, thanks a lot. But... which is the motivation of this approach?
Why a "standard" version of the TSS is not given as the one you
obtain if the regression is run "by hand"?
I think we're talking about WLS here, and the fact that gretl (as R)
uses the "weighted TSS" when computing certain auxiliary statistics.
I don't wish to claim this method is uniquely correct, but it
clearly makes some sense. In the WLS regression the "constant" is
not actually constant, and for the purpose of testing the overall
specification the null model arguably should not include a true
constant either, but rather the non-constant weighted transformation
of a sequence of 1s. That's just what using the "weighted TSS"
achieves.
Allin
4:03 p.m.
On Tue, 18 Jun 2019, Sven Schreiber wrote:
Am 18.06.2019 um 17:12 schrieb javier.garcia(a)ehu.es:
> Hello everybody;
Hi Javier,
> I would like to make a suggestion regarding the FGLS/WLS estimator
> implementation in Gretl.
>
> When we have a model where the errors present autocorrelation (for example,
> an AR(1) process), and we try to get the estimated model this way:
> Model->Time Series->AR errors (GLS) -> AR(1), some post-estimation
> tests/results… are disabled. In particular, no autocorrelation and/or
> heteroskedasticity tests can be implemented (Tests->Heteroskedasticity or
> Tests->Autocorrelation).
1) heterosk.: in a time-series context you typically would test for the
ARCH-variant, and that is available.
2) autocorrelation: What you're saying sounds natural at first, but
guess what other software are saying when you ask for such a diagnostic
test after AR-estimation: "Not available with this estimation method
(ARMA ML)." (This is from Eviews 10.) You do get the residual
correlogram and the Q-stats.
Just to amplify Sven's comment: In gretl, $uhat gives the GLS
residuals, and under the Graphs menu in the model window you have the
"Residual correlogram" option, which shows both the ACF and PACF plots
and Q-statistics up to a chosen lag.
In addition, the output of "Statistics based on the rho-differenced
data" shows rho and Durbin-Watson for the GLS residuals.
Finally, you can save $uhat (Save menu, Residuals), regress it on a
constant, and run an autocorrelation test of your choice.
So there's no shortage of means of checking that the GLS residuals are
white noise.
Allin
11:55 p.m.
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".
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?
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).
Thanks a lot in advance.
Best
Javi
9:24 a.m.
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
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Allin Cottrell -
javier.garcia＠ehu.es -
Sven Schreiber