[Gretl-users] Re: Wald test for BEKK-GARCH coefficients
On Mon, 1 Feb 2021, Sven Schreiber wrote:
I'm certainly not an expert in the MGARCH package (which you
appear to
be using here), I'm just going by its help text here (which is not very
detailed as the package declares itself work in progress, even though we
know that the progress has basically stalled).
True. I do have some code I've got to integrate into the package (for
example, offering the DCC model as well as the BEKK model), but I never
find the time for this, sorry. If anyone's interested in helping me,
please speak up!
So I guess you want to test that both of these coefficients are
zero,
and the standard formulation is $H_0: R \theta = 0$, where R has two
rows (unit vectors here) and \theta is the coefficient vector. Then
you should be able to apply the standard Wald test quadratic form
(https://en.wikipedia.org/wiki/Wald_test) by plugging in Modelbekk.coeff
for the theta estimate and Modelbekk.vcv for Vhat (and of course a zero
vector for r).
Something like this (where a and b are the position of the elements you
want to test):
<hansl>
function scalar WaldTest(matrix coeff, matrix vcv, scalar a, scalar b)
R = zeros(2, rows(coeff))
R[1, a] = 1
R[2, b] = 1
outside = R*coeff
inside = qform(R, vcv)
return qform(outside', inv(inside))
end function
## example
coeff = mnormal(10,1)
V = I(10)
W = WaldTest(coeff, V, 2, 6)
</hansl>
Note: the code here could be optimised, but I went for maximum clarity.
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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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