Re: [Gretl-users] Cointegration with Gretl -Suggestions!
On Wed, February 8, 2006 22:15, john w wrote:
I'm giving a suggestion. Listen carefully-as you said a VECM is a
VAR VAR
with nonlinear restrictions. This is well solved in PcGive. When selecting
data which enter in VAR ( which will be the basis to determine the number of
cointegration rank for future VECM) you can choose if constant and trend
will be unrestricted or restricted i.e. exogenous. This means that you can
enter (in a VAR model) constant as unrestricted but also as exogenous. This
stays for trend too.
So, you are getting Johansen cases:
Const, Trend - all as restricted
Const - unrestricted, Trend - restricted
Const - restricted, Trend - unrestricted etc.
After such estimation in which you can determine the constant and trend to
be unrestricted or not you procede with usual VAR model and usual testings.
This results are then applyed for VECM estimation.
I don't understand. Allow me some LaTeX-speak to be clearer; assume your VECM
can be written this way:
\Delta y_t = \mu + \alpha \beta' y_{t-1} + \epsilon
where y_t has n rows and r is the cointegration rank, so \alpha and \beta are
(nxr) matrices.
When you restrict eg the constant in a vecm, you force it into the space
spanned by the columns of \alpha. In other words, you hypothesize that the
(nx1) vector \mu can be written as \alpha \cdot m, where m is an unrestricted
(rx1) vector. As a consequence, you're imposing (n-r) constraints. In an
unrestricted VAR, r=n; I fail to see how you can restrict the constant in an
otherwise unrestricted VAR.
Maybe my poor understanding of cointegration is showing? :-)
--
Riccardo "Jack" Lucchetti
Dipartimento di Economia
Facoltà di Economia "G. Fuà"
Ancona