Re: [Gretl-users] Deterministic trend in VAR
On Tue, 13 Dec 2011, Muheed Jamaldeen wrote:
JMULTI computes modulus of the eigenvalues
of the reverse characteristic polynomial which are all greater than one
(which is the stability condition, implying stationarity).
[...]
Also, for consistency I computed the VAR inverse roots on Gretl. They
are
all inside the unit circle. Implying stability of the VAR process.
You cannot decide on the number of unit roots in a VAR simply by looking
at the estimated eigenvalues (unless you happen to have magical powers,
but in that case you don't need econometrics at all). This is because the
properties you cite hold for the TRUE eigenvalues (whatever that means),
but you only see their estimates, which are different with probability 1.
In most cases, estimated eigenvalues do converge in probability to the
true ones, because of consistency of the VAR estimated coefficients and
the fact that eigenvalues are a continuous function of the companion
matrix, so you can invoke the continuous mapping theorem, but their
asymptotic distribution is decidedly weird. I remember reading a paper a
few years ago about the fact that if you estimate a VAR(p) over white
noise data, the aymptotic properties of the estimated eigenvaules are
such that, as p grows, you're bound to find them uniformly scattered
AROUND THE UNIT CIRCLE. Actually, I can't find the paper right now, so I'd
be grateful if anybody could give me a pointer (and yes, I've already
googled for it).
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti