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