Dear Sir,
I am building an assymteric BEKK model with the following. I would like to have the probability of negative residuals using the following codes below. The following paper: Trading with asymmetric volaility spillovers by angel pardo & hipolit torro adapted a porbability of 0.5. Their paper indicated that assymetry coefficient is 0.50 whilst the assymetry cross-coefficient is 0.5*0.5. I don't know how it was built into the folllwing code or it hads already been done?
Hope to get clarification. Many thanks.
nonlin(parmset=distparms) nu
function VTSign v s
type vector v s VTSign
*
local integer i
*
dim VTSign(%rows(v))
ewise VTSign(i)=%if(%sign(v(i))==s(i),v(i),0.0)
end
*
compute signs=||-1.,-1.||
declare series[symm] uus
gset uus gstart gend = %zeros(n,n)
*
frml logl = $
hx = hf(t) , $
%do(i,1,n,u(i)=resid(i)) , $
ux = %xt(u,t), $
h(t)=hx, uu(t)=%outerxx(ux), $
uus(t)= %outerxx(VTSign(ux,signs)), $
%logtdensity(hx,ux,nu)
assymteric in BEKK model
Re: assymteric in BEKK model
They're doing just a standard asymmetric BEKK. The .5 simply refers to the fact that the probability of a negative shock is assumed to be .5. However, their calculation of the contribution of the asymmetric term to the VIRF for s>1 isn't correct---you can't just take the matrix and multiply by .5. That works for the diagonal terms (variances) but not the off-diagonal terms. The expected value for an off-diagonal is (under the assumption of Gaussian residuals)
sigma12*PHI(0,0,rho)+sqrt(1-rho^2)/(2pi)*sqrt(sigma11*sigma22)
where PHI is the bivariate CDF for correlated standard Normals and rho is the correlation coefficient. The .5 x sigma12 is roughly correct for rho very near one (almost all the mass is in the northeast and southwest quadrants, equally distributed), but quite wrong for rho near -1, where there is almost no probability of the two having the same signs so this reduces to zero.
There is no general distribution-free value for this.
sigma12*PHI(0,0,rho)+sqrt(1-rho^2)/(2pi)*sqrt(sigma11*sigma22)
where PHI is the bivariate CDF for correlated standard Normals and rho is the correlation coefficient. The .5 x sigma12 is roughly correct for rho very near one (almost all the mass is in the northeast and southwest quadrants, equally distributed), but quite wrong for rho near -1, where there is almost no probability of the two having the same signs so this reduces to zero.
There is no general distribution-free value for this.