Re: [Gretl-users] Help with GIG package
On Tue, 8 Mar 2011, cociuba wrote:
Deal Gretl Community,
I am trying to replicate the examples in Principles of Econometrics,pg.373, BYD example,
using Garch in Gretl
(GIG). I was able to reproduce those result with Lee Adkins scripts but I cant do the
same using GIG.
My questions are:
- what I'm suppose to put in mean and variance regressors list to obtain the
following models:
TGARCG(1,1) and Garch in Mean.
- are there any other manual or examples using GIG gui beside those found on Ricardo
Lucchetti's home page.
There's a fundamental notation problem here.
Lee's book follows the notation in Hill et al, which in turn is based on
what I believe EViews uses. The trouble is that what EViews calls a TGARCH
is not the same thing as what gig calls a TARCH. The model described in
eq. 14.9 in Lee's book corresponds to what gig calls a GJR model, with
different notation.
Lee's TARCH:
h_t = delta + alpha_1 e_{t-1}^2 + gamma d_{t-1} e_{t-1}^2 + beta_1 h_{t-1}
Gig's GJR:
h_t = omega + alpha (|e_{t-1}| - gamma e_{t-1})^2 + beta h_{t-1}
so the correspondence between Eviews notation and gig notation is
delta = omega
alpha_1 = alpha * (1-gamma)^2
gamma = 4 * alpha * gamma
beta_1 = beta
If you use gig to estimate a GJR model, you get:
omega 0.356018 0.0723963 4.918 8.76e-07 ***
alpha 0.476325 0.0760667 6.262 3.80e-10 ***
gamma 0.257023 0.0705906 3.641 0.0003 ***
beta 0.286992 0.0700316 4.098 4.17e-05 ***
The above, in the Eviews parametrisation, would give
delta 0.35602
alpha 0.26294
gamma 0.48971
beta 0.28699
which is roughly what you get in Lee's book.
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti