Re: [Gretl-users] small conflict in multiplicative ARMA
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