Re: [Gretl-users] Deterministic terms in VEC models
On Fri, 18 Sep 2015, Stefan A. wrote:
Dear fellow gretl users,
I have two questions about deterministic trends in VEC models.
gretl offers the five traditional approaches to VEC modelling, either
omitting all deterministic terms or including constants and trends in
restricted and unrestricted combinations. I was wondering if there are any
good "rules of thumb" for when to choose which approach? The EViews manual,
for example, suggests choosing a model with constant + restricted trend if
some of the level variables appear to oscillate around a linear trend, I
believe (although my memory may serve me wrong here).
Also, from the gretl manual I learned that the specification of a VEC model
with a constant and *restricted* trend looks like this (LaTeX code):
$\Delta y_{t}=\mu_{0}+\mu_{1}t+\alpha\beta'y_{t-1}+
\sum_{i=1}^{p-1}\Gamma_{i}\Delta y_{t-i}+\epsilon_{t}$
where $\alpha'\perp\mu_{1}=0$
I was wondering how the restriction of alpha being orthogonal to mu is
achieved in practice?
Thanks in advance for your help!
Both your questions have their full answer in any good general time series
econometrics textbooks (Hamilton, Lütkepohl, Martin et al, ...) or in
books that deal specifically with the VECM model (eg Johansen, Juselius).
However, in brief: what you call Eviews' rule of thumb is not Eviews' and
is not a rule of thumb. Out of the canonical "five cases", the only two
consistent with the observed data going steadily up (or down) are cases 3
and 4 (u. const. and r. trend, respectively); but then, case 4 is
preferable for quite a few reasons that it would take too long to explain
here.
As for the "alpha orthogonal restriction", it can be shown that the
computation is nearly immediate by augmenting the vector of lagged levels
with the appropriate determinsitic terms when computing the
eigendecomposition which lies at the heart of Johansen's ML approach. More
detail in the books I listed above.
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Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
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