Volatility IRF

[fadimohamed]

Dear Tomm,
I have a question with regard to setting the initial values for the variances, taking into account that i am using an asymmetric BEKK representation GARCH(1,1), should i use the long-run unconditional variance equation? Is there a way to consider the asymmetry effects in it?
Many Thanks
Fadi

[TomDoan]

With asymmetry, there is no closed-form stationary solution for the variance for any non-trivial multivariate GARCH model because the expected value of the asymmetric term is a non-linear function of the covariance matrix. The following solves the system of non-linear equations by converting into VECH form and using a Gauss-Seidel algorithm (which just replaces the estimate with the RHS calculation looking for a stationary point). Note that it's possible that this won't converge if there is no stationary solution among positive definite matrices.

The procedure for converting to the VECH representation is posted at:

http://www.estima.com/forum/viewtopic.php?f=7&t=1433

This requires at least RATS 7.3 because it uses the %BICDF function.

Code: Select all

open data m-pfemrk6508.txt
calendar(m) 1965:1
data(format=prn,org=columns) 1965:01 2008:12 date pfe mrk
*
garch(p=1,q=1,mv=bekk,asymmetric,piters=10,pmeth=simplex,iters=200) / pfe mrk
*
@MVGARCHtoVECH(MV=BEK,asymm)
compute ncomp=%symmpos(%nvar,%nvar)
dec vect hvech(ncomp)
dec symm h0(%nvar,%nvar) hasymmsq(%nvar,%nvar)
ewise h0(i,j)=%if(i==j,%%vech_c(%symmpos(i,j)),0.0)
do iters=1,100
   compute rmatrix=%cvtocorr(h0)
   ewise hasymmsq(i,j)=rho=rmatrix(i,j),%if(i==j,.5*h0(i,i),$
     h0(i,j)*%bicdf(0.0,0.0,rho)+sqrt(1-rho^2)/(2*%pi)*sqrt(h0(i,i)*h0(j,j)))
   compute hvech=%vec(h0)
   compute hvech=%%vech_c+%%vech_a*hvech+%%vech_b*hvech+%%vech_d*%vec(hasymmsq)
   compute h0=%vectosymm(hvech,%nvar)
   disp hvech
end do iters


m-pfemrk6508.txt

Data file

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