4:36 p.m.
First of all, kudos to Allin and the development team for making an
ARIMA (as opposed to ARMA) routine available in the latest version of
gretl! I personally find this of immense utility in my classes as
students do not have to back calculate raw level forecasts from
differenced data.
Now, on the bleaker side, I seem to face some problems with the routine.
First of all you may download my test file from
http://paravantis.com/cars100.gdt
(It represents the number of cars per 100 people in Greece from 1970 to
2003.)
The data set includes 3 columns: Cars100 (cars per 100 people), DIFF1_Ca
(1st differences) and DIFF2_Ca (2nd differences). Now, in the past Allin
indicated to me that he felt that taking the 2nd differences of Cars100
was probably OVERDIFFERENCING. Yet, using correlograms and taking into
account which of these series has the SMALLEST STANDARD DEVIATION, I
think that the second differences are "best" (and it is kept in mind
that mild underdifferencing may be corrected with more AuroRegressive
terms while mild overdifferencing may be corrected with more Moving
Average terms).
Coming now to the crunch of the matter, there appear to exist QUITE A
FEW ARIMA models that CANNOT be estimated with gretl which gives a
dialog box stating "The convergence criterion was not met".
UNFORTUNATELY, there is NO OPTION to increase the number of iterations
(or make the convergence threshold more lax). These models include:
ARIMA(1,2,1)
ARIMA(0,2,1)
It should be noted that these models MAY BE ESTIMATED with X-12_ARIMA
but not with the "default" ARIMA routine.
Here is what I would appreciate having as feedback from the respected
gretl community:
1. How do you stand on the differencing issue? Do you side with 1st or
2nd differences? Does it really matter since we can "correct" by
including more AR or MA terms?
2. What causes the problem with the default ARIMA routine? Is it "safe"
to use X-12-ARIMA in all cases (even with unseasonal data)?
Thanking you all for you time,
John Paravantis
University of Piraeus
Greeece
3:47 p.m.
El Jueves, 30 de Marzo de 2006 18:36, John Paravantis PhD escribió:
...
Now, on the bleaker side, I seem to face some problems with the routine.
First of all you may download my test file from
http://paravantis.com/cars100.gdt
(It represents the number of cars per 100 people in Greece from 1970 to
2003.)
I think you have few observations to work with standard time series tecniques.
In ARIMA models you do not have unbiadness in the estimators, you only have
consistency, and this is a property that justifies good estimations only with
a large number of observations. The sample correlograms are only consistent
as well, so you may not trust in them with so few observations.
Few observations produces large standard deviations of the coefficients so the
estimations have a large variance (they are very inaccurate) and all the
tests tend to be not rejected.
Coming now to the crunch of the matter, there appear to exist QUITE
A
FEW ARIMA models that CANNOT be estimated with gretl which gives a
dialog box stating "The convergence criterion was not met".
UNFORTUNATELY, there is NO OPTION to increase the number of iterations
(or make the convergence threshold more lax). These models include:
ARIMA(1,2,1)
ARIMA(0,2,1)
It should be noted that these models MAY BE ESTIMATED with X-12_ARIMA
but not with the "default" ARIMA routine.
I think the problem here is that you have so few observations and the variance
of the coefficient estimator is so large that the change in the estimations
from one iteration to the following is so large that gretl cannot converge.
I asked in a previous message to this list to have a method for changing the
number of iterations. You may read the response in
http://ricardo.ecn.wfu.edu/pipermail/gretl-users/2006-February/000499.html
but I think probably this will not work in your case.
Here is what I would appreciate having as feedback from the respected
gretl community:
1. How do you stand on the differencing issue? Do you side with 1st or
2nd differences? Does it really matter since we can "correct" by
including more AR or MA terms?
Apart form the graphics (and with your graphic I would vote for I(2)), we
normally use a test (as ADF: in /variable/augmented Dickey-Fuller test) but
with your data you will see that all the tests are not rejected, and this is
only because your data have no enough information.
2. What causes the problem with the default ARIMA routine?
Too few observations.
Is it "safe"
to use X-12-ARIMA in all cases (even with unseasonal data)?
No. In some cases you may obtain an estimation, but in your case you may not
trust in it because you have a very large variance.
--
Ignacio Díaz-Emparanza
Dpto. de Economía Aplicada III (Econometría y Estadística)
UPV-EHU
6824
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