12:51 p.m.
Hi,
I am trying to measure the volatility spillover effect from S&P500 to FTSE100 using
bivariate BEKK-GARCH model. My code inp and outputs are forwarded to the email.
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.
My codes are:
set verbose offlist returns = spx_return ftse_returnscalar VAR_lags = 1list VAR_exog =
constbundle Modelbekk = BEKK_setup(returns, VAR_lags,
VAR_exog)BEKK_estimate(&Modelbekk, 10)BEKK_printout(&Modelbekk)
5:16 p.m.
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
4:21 a.m.
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.
-------------------------------------------------------
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
-------------------------------------------------------
4:47 a.m.
Am 02.02.2021 um 10:21 schrieb Riccardo (Jack) Lucchetti:
On Mon, 1 Feb 2021, Sven Schreiber wrote:
> 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):
Jack, so what about the A and B matrices, is that universal notation in
that area such that indeed those are the wanted coefficients for the
spillover hypothesis?
thanks
sven
4:51 a.m.
On Tue, 2 Feb 2021, Sven Schreiber wrote:
Am 02.02.2021 um 10:21 schrieb Riccardo (Jack) Lucchetti:
> On Mon, 1 Feb 2021, Sven Schreiber wrote:
>> 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):
Jack, so what about the A and B matrices, is that universal notation in
that area such that indeed those are the wanted coefficients for the
spillover hypothesis?
Yes, in the BEKK literature those matrices are universally called A and B.
-------------------------------------------------------
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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4 comments
3 participants
participants (3)
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Burak Korkusuz -
Riccardo (Jack) Lucchetti -
Sven Schreiber