10:58 a.m.
Hello everybody (although this is specially directed to Jack and Allin)
I was playing with the ARMA dialog box for seasonal models, and I found and
small conflict with the names of the coeffients that gretl assigns in the
output. If I estimate an AR(1)xAR(1)s : (in Latex)
(1-\phi_1L)(1-\Phi_1L^s)Y_t=\epsilon_t
with, for example, quarterly data, the model output reports the coefficients
with names: varname(-1) and varname(-4) which is slightly confusing since the
coeffients of the above multiplicative model are not directly associated to
an specific lag of the dependent variable. Furthermore, if I estimate an
AR(4)xAR(1)s, gretl gives an error, since following the rule, it has to
assign the same name to the fourth AR(4) coefficient and the unique AR(1)s
one. (I obtain: "memory fault error"). Exactly the same occurs with the MA
part.
So I suggest to change the name of the coeffients in the model output:
as the literature is quite standard referring to these coefficients as \phi
and \theta, we could use phi_1, phi_2 etc for the regular AR part, and
sphi_1, sphi_2 etc (or Phi_1, Phi_2, ... with less characters) for the
seasonal part; theta_1, theta_2, ... for the regular MA and stheta_1,
stheta_2 ... for the seasonal MA.
This change is not needed for a non-seasonal model, but could be adopted for
maintaining homogeneity if you want.
--
Ignacio Díaz-Emparanza
Dpto. de Economía Aplicada III (Econometría y Estadística)
UPV-EHU
4:01 p.m.
On Thu, February 16, 2006 11:58, Ignacio Díaz-Emparanza wrote:
Hello everybody (although this is specially directed to Jack and
Allin)
I was playing with the ARMA dialog box for seasonal models, and I found and
small conflict with the names of the coeffients that gretl assigns in the
output. If I estimate an AR(1)xAR(1)s : (in Latex)
(1-\phi_1L)(1-\Phi_1L^s)Y_t=\epsilon_t
with, for example, quarterly data, the model output reports the coefficients
with names: varname(-1) and varname(-4) which is slightly confusing since the
coeffients of the above multiplicative model are not directly associated to
an specific lag of the dependent variable.
I think that, with gretl as-is, the seasonal AR operator just sticks the
s-lagged dependent variable into the conditional mean specification, which of
course is not right from your viewpoint. If you expand the lag polynomial in
your example, you get
(1 - \phi_1 L - \Phi_1 L^s + \phi_1 \Phi_1 l^{s+1}) Y_t = \epsilon_t
which is an ordinary autoregressive model (with some "holes" in), subject to a
nonlinear constraint.
If you don't need an MA part, you can estimate your model via nls like this
(suppose s = 4):
# initialize by OLS
ols y const y(-1) y(-4) y(-5)
scalar m = $coeff(const)
scalar phi = $coeff(y_1)
scalar Phi = $coeff(y_4)
# estimate via nls
nls y = m + phi*y(-1) + Phi*y(-4) - phi*Phi*y(-5)
end nls
Is this what you have in mind?
Furthermore, if I estimate an
AR(4)xAR(1)s, gretl gives an error, since following the rule, it has to
assign the same name to the fourth AR(4) coefficient and the unique AR(1)s
one. (I obtain: "memory fault error"). Exactly the same occurs with the MA
part.
I'm not sure I understand here. Could you post your results?
So I suggest to change the name of the coeffients in the model
output:
as the literature is quite standard referring to these coefficients as \phi
and \theta, we could use phi_1, phi_2 etc for the regular AR part, and
sphi_1, sphi_2 etc (or Phi_1, Phi_2, ... with less characters) for the
seasonal part; theta_1, theta_2, ... for the regular MA and stheta_1,
stheta_2 ... for the seasonal MA.
I like this.
--
Riccardo "Jack" Lucchetti
Dipartimento di Economia
Facoltà di Economia "G. Fuà"
Ancona
5:47 p.m.
El Jueves, 16 de Febrero de 2006 17:01, escribió:
I think that, with gretl as-is, the seasonal AR operator just sticks
the
s-lagged dependent variable into the conditional mean specification, which
of course is not right from your viewpoint. If you expand the lag
polynomial in your example, you get
(1 - \phi_1 L - \Phi_1 L^s + \phi_1 \Phi_1 l^{s+1}) Y_t = \epsilon_t
which is an ordinary autoregressive model (with some "holes" in), subject
to a nonlinear constraint.
If you don't need an MA part, you can estimate your model via nls like this
(suppose s = 4):
# initialize by OLS
ols y const y(-1) y(-4) y(-5)
scalar m = $coeff(const)
scalar phi = $coeff(y_1)
scalar Phi = $coeff(y_4)
# estimate via nls
nls y = m + phi*y(-1) + Phi*y(-4) - phi*Phi*y(-5)
end nls
Is this what you have in mind?
Yes, and I think this is what Gretl should calculate with the "arma" command.
From Box and Jenkins (see Box,Jenkins and Reinsel book chapter 9, page
332)
this is the standard way to include seasonality in an ARMA model.
> Furthermore, if I estimate an
> AR(4)xAR(1)s, gretl gives an error, since following the rule, it has to
> assign the same name to the fourth AR(4) coefficient and the unique
> AR(1)s one. (I obtain: "memory fault error").
Sorry, not very exact
Spanish to English translation. The gretl english
version gives "out of memory error".
> Exactly the same occurs
> with the MA part.
I'm not sure I understand here. Could you post your results?
Obviously, I do not have results. I thought gretl was estimating a "truely"
multiplicative model as above. So I hoped to obtain
phi_1, phi_2, phi_3, phi_4 and Phi_4 being Phi_4 (seasonal coeff) different to
phi_4. In a multiplicative MA(4)xMA(1)s
Y_t=(1-\theta_1 L- ... - \theta_4 L^4)(1-\Theta_1 L^4)\epsilon_t
I suppose the same is happening, gretl has a problem with the naming of
coeffs: e(-1), e(-2), e(-3), e(-4) and, so it is not possible to use again
e(-4) for the seasonal.
--
Ignacio Díaz-Emparanza
Dpto. de Economía Aplicada III (Econometría y Estadística)
UPV-EHU
6:16 p.m.
On Thu, 16 Feb 2006, Riccardo Jack Lucchetti wrote:
I think that, with gretl as-is, the seasonal AR operator just
sticks the s-lagged dependent variable into the conditional mean
specification, which of course is not right from [Ignacio's]
viewpoint.
Yes, I can confirm that is the current state of things. Looks like
this needs some work.
Allin.
6:29 p.m.
On Thu, February 16, 2006 19:16, Allin Cottrell wrote:
On Thu, 16 Feb 2006, Riccardo Jack Lucchetti wrote:
> I think that, with gretl as-is, the seasonal AR operator just
> sticks the s-lagged dependent variable into the conditional mean
> specification, which of course is not right from [Ignacio's]
> viewpoint.
Yes, I can confirm that is the current state of things. Looks like
this needs some work.
Allin.
Ignacio, you're 100% right. Allin, I have a couple of ideas on how to modify
the code. Before I start, though, I'd like to ask everybody if they would
object to having seasonal AR/MA parts like an "on/off switch" rather than
specifying an order. That would make for much cleaner code; we wouldn't have
the option of a seasonal stucture like (1 - \Phi_1 L^s - \Phi_2 L^{2s}). It
can be done, but the code would come out much uglier (unless Allin has a
brilliant programming solution --- not unlikely).
--
Riccardo "Jack" Lucchetti
Dipartimento di Economia
Facoltà di Economia "G. Fuà"
Ancona
6:39 p.m.
On Thu, 16 Feb 2006, Riccardo Jack Lucchetti wrote:
Ignacio, you're 100% right. Allin, I have a couple of ideas on
how
to modify the code. Before I start, though, I'd like to ask
everybody if they would object to having seasonal AR/MA parts like
an "on/off switch" rather than specifying an order. That would
make for much cleaner code; we wouldn't have the option of a
seasonal stucture like (1 - \Phi_1 L^s - \Phi_2 L^{2s}). It can be
done, but the code would come out much uglier (unless Allin has a
brilliant programming solution --- not unlikely).
One quick observation. If you use the x-12-arima option with arma
in gretl, you'll get the correct multiplicative model. At present
that will still have the problem of naming of coefficients, noted by
Ignacio, if the non-seasonal order is long enough to "bump into" the
seasonal component. But that issue should be quickly fixable.
As a temporary measure, I can fix the naming issue and perhaps
arrange that when mixed seasonal/non-seasonal arma is specified, we
just use x-12-arima.
Allin.
9:57 p.m.
New subject: Seasonal ARMA fix
I wrote:
As a temporary measure, I can fix the naming issue and perhaps
arrange that when mixed seasonal/non-seasonal arma is specified,
we just use x-12-arima.
That's now done, in CVS and in today's Windows snapshot. We'll work
on getting gretl's native ARMA code into multiplicative mode
shortly.
Allin.
3:04 a.m.
New subject: seasonal ARMA again
Thanks to Ignacio for noting some problems in this regard.
I now realize, however, that I was wrong to say that gretl's ARMA
code is not set up to handle the multiplicative relationship between
the non-seasonal and seasonal components. Pardon the double
negative -- to put it positively, gretl's ARMA code _is_ in fact
already set up to handle the multiplicative relationship, but it had
some bugs, which I have now tried to fix.
Tomorrow (Feb 17) I will make both a new Windows snapshot and a new
gtk2 rpm snapshot. I would very much appreciate if people with more
expertise in this area than myself could do some testing.
For reference, I'm including a script that I've used for basic
testing here. It generates an artificial series that follows a
known ARMA (1,1)(1,1)s process then uses both the gretl native and
X-12-ARIMA ARMA routines to try to retrieve the parameters.
If I'm misunderstanding how this ought to work, that should be
apparent from the script!
# Seasonal ARMA test script
nulldata 1200
setobs 12 1920:01
scalar phi_1 = 0.5
scalar Phi_1 = 0.1
scalar theta_1 = 0.2
scalar Theta_1 = 0.2
genr eps = normal()
# Artificial error process
genr u = eps + theta_1*eps(-1) + Theta_1*eps(-12) \
+ theta_1*Theta_1*eps(-13)
series y = 0
# Artificial seasonal series
genr y = 500 + phi_1*y(-1) + Phi_1*y(-12) \
- phi_1*Phi_1*y(-13) + u
# Estimate using native ARMA code
arma 1 1 ; 1 1 ; y
# Compare X-12-ARIMA estimates -- but note that X-12-ARIMA
# can only handle 720 observations, so we truncate the data
smpl +500 ;
arma 1 1 ; 1 1 ; y --x-12-arima
Allin Cottrell
6907
days inactive
6908
days old
7 comments
3 participants
participants (3)
-
Allin Cottrell -
Ignacio Díaz-Emparanza -
Riccardo Jack Lucchetti