bekk parameters

[luxu1983]

dear
in the bekk model ,the parameters can not be interpreted on an individual basis
the functions of the parameters form the coeffecient of lagged variance ,covariance..
how to calculate the standard error of function of estimated coefficients using RATS?

[TomDoan]

SUMMARIZE can compute standard errors of arbitrary functions of parameters using the delta method.

[myousefi1360]

how can i use SUMMARIZE command as input command to my estimation.
i entered SUMMARIZE after the estimation of bivariate BEKK GARCH (1,1) but i did not get any output. how can i apply this command to get coefficent of variables in each variation equation?

[vinayadhikari]

I have the exact same question. My adviser told me that I don't have to worry about interpreting the coefficients. Rather, I should interpret the impulse response. I would be grateful if you could elaborate both on how to get the impulse responses and how to implement the SUMMARIZE command.

One example code will probably be sufficient. Thanks.

[mengqi]

Hi Tom,

May I ask how to SUMMARIZE the standard error results using the delta method?

Thanks.

[TomDoan]

For a BEKK model, you can do something like:

Code: Select all

dec vect means(%nregmean)
dec packed cx(%nvar,%nvar)
dec rect ax(%nvar,%nvar) bx(%nvar,%nvar)
nonlin(parmset=garchparms) means cx ax bx

summarize(parmset=garchparms) ax(1,1)^2
summarize(parmset=garchparms) ax(1,1)*ax(1,2)*2.0
summarize(parmset=garchparms) ax(1,2)^2

Different types of multivariate GARCH models have different forms for the C, A and B matrices, and so will have a different PARMSET set up, but the BEKK is generally the only one where non-linear functions of the underlying parameters have any real interest.

[mengqi]

dear Tom,

is the PARMSET set up the same for DCC model when i use SUMMARIZE?

bests

[TomDoan]

dear Tom,

is the PARMSET set up the same for DCC model when i use SUMMARIZE?

bests

No. It would depend upon what the variance model is. What would you want to do with that anyway? What function of the parameters would be of any interest with that?

[humyra]

Wow! This is absolutely amazing! Thanks for correcting it.

One last thing, if I want to multiply the bekk-garch output I've obtained to give the three variance equations, what code should I use?

[TomDoan]

That's three equations each with ten terms for a bivariate asymmetric BEKK, and no one will ever read them---it's harder to make sense out of model in that form then it is in the original form. The above calculated the three coefficients in the A component for explaining h(1,1). You have similar set of three calculations for the A part of h(1,2) and another three for h(2,2). Then the same set of nine for the B terms and another set for the D terms. And three for the variance constants.

If you really want to do this, this organizes a calculation for the standard errors of the A terms in the VECH representation. You would need to do the same thing for B's and D's.

Code: Select all

compute ncomp=%nvar*(%nvar+1)/2
dec rect %%vech_ase(ncomp,ncomp)
do m=1,ncomp
   do n=1,ncomp
      compute i=%symmrow(m),j=%symmcol(m),$
              k=%symmrow(n),l=%symmcol(n)
      if k==l {
         summarize(noprint,parmset=garchparms) ax(i,k)*ax(j,l)
         compute %%vech_ase(m,n)=sqrt(%varlc)
      }
      else {
         summarize(noprint,parmset=garchparms) $
             ax(i,k)*ax(j,l)+ax(i,l)*ax(j,k)
         compute %%vech_ase(m,n)=sqrt(%varlc)
      }
   end do n
end do m