[Gretl-users] Re: Wald test for BEKK-GARCH coefficients
Am 01.02.2021 um 18:51 schrieb Burak Korkusuz:
The volatility spillover effect is measured as the sum of the
off-diagonal coefficients of the variance equation matrices A and B,
which is E[1,2] = |A[1,2]| + |B[1,2]|.
Next, I need do the Wald test to test the off-diagonal coefficients?
(whether they are significant or not; meaning there is volatility
spillover from sp500 to ftse or not). I do not know how to write the
codes for the Wald test to following my codes (I am not good at coding
that much, i usually use drop-down menu but i see it is not available in
my case).
Does anyone know how to write Wald test codes to following below codes?
I am not familiar with coding stuff and bundle context that's why I am
asking here.
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). Also I have no idea about
the notation that is used.
Let's make the assumption that the A and B matrices you are mentioning
in your formula above are the same A and B matrices in the output. (This
assumption could be completely wrong!)
My codes are:
set verbose off
list returns = spx_return ftse_return
scalar VAR_lags = 1
list VAR_exog = const
bundle Modelbekk = BEKK_setup(returns, VAR_lags, VAR_exog)
BEKK_estimate(&Modelbekk, 10)
BEKK_printout(&Modelbekk)
Then you would be interested in the bundle members Modelbekk.coeff and
Modelbekk.vcv. Given a bivariate system (N=2) I think B[1,2] would be
the penultimate element of coeff and A[1,2] would be 6th from the back.
(You can verify that by comparing the numbers in those vectors with the
printed output.)
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).
HTH,
sven