Re: [Gretl-users] $vma accessor details
On Thu, 20 Jul 2017, Sven Schreiber wrote:
Hi,
about the $vma (vector moving-average) accessor the user guide says (p. 235
of the A4 version):
"the $vma accessor returns an (h + 1) × n^2 matrix, in which the (i + 1)-th
row is the vectorized form of Θ_i"
(and this latter \Theta_i is a VMA coeff matrix in the math equation)...
I'm wondering whether "vectorized" means by row or by column. So is
$vma[i+1,
] equal to transp(vec(Theta_i)), or equal to transp(vec(transp(Theta_i))) ?
The rows of $vma are arranged in such a way that you can mshape the result
and it "come out right". In the following example, we generate a
triangular VAR, so that the VMA polynomial is also lower-triangular and
the corresponding estimate is near-zero:
<hansl>
nulldata 1000
series x = normal()
series y = normal()
x = 0.99*x(-1) + normal()
y = 0.99*y(-1) + 0.99*x(-1) + normal()
var 1 x y
V = $vma
print V
V_3 = mshape(V[4,], 2, 2)
print V_3
</hansl>
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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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