multivariate VAR-CCC model with modified variance equations

[tunelbana2]

Dear Tom,

I have a question for you. From some time I am trying to find a software with could help me estimate VAR-CCC model with a couple of modifications. Generally, I am basing on article "VOLATILITY TRANSMISSION FOR CROSS LISTED FIRMS AND THE ROLE OF INTERNATIONAL EXPOSURE" written by Bartolomé Pascual-Fuster and Jorge V. Pérez-Rodríguez (article attached). As I know, they used Rats to estimate this model.

As I know the official code to estimate VAR-CCC is:
system(model=var1)
variables x y
lags 1
det constant
end(system)
garch(p=1,q=1,model=var1,mv=cc)

But I need to create a code to estimate following specification:

VAR: (as it is shown on page no 1) for p1=p2=1


|r(1,t) | = | a(1,0) | + | b(21,0) * r (2,t) + b(11,0) * r (1, t-1) + b(21,1) * r (2,t-1) + b(11,1) * r (1, t-2) | + | e (1,t) |
|r(2,t) | | a(2,0) | | b(12,0) * r (1,t-1) + b(22,0) * r (2, t-1) + b(12,1) * r (1,t-2) + b(22,1) * r (2, t-2) | | e (2,t) |



This Var statement is based on assumption that we have 2 markets totaly non-overlapping. Market nr 1 (USA is opening as a second market) and market no 2 (Japan is opening first), so the informations generated on market 2 in day t (r(2,t)) are available for market 1 in the same day. So there is a problem with different lags in both equations.


CCC equations are: (as it is shown on page no 2) for z1=z2=0

h(1,t) = a(1) + b(1) * h(1, t-1) + c(21,0) * e^2(2,t) + c(11,0) * e^2(1,t-1)
h(2,t) = a(2) + b(2) * h(2, t-1) + c(12,0) * e^2(1,t-1) + c(22,0) * e^2(1,t-1)
h(12,t) = rho(12) * sqrt( h(1,t)*h(2,t) )


Could you please help me with this code?

Thank You!
Joanna

[TomDoan]

You can't use a VAR setup because the equations are different. This would be similar to a two variable version of what's done in the paper. Obviously, the mean equations could be altered somewhat---this is set up to do what they do, which is to include two "lags" of each variable, either {0 1} or {1 2}, and similarly to include one u^2 term for each in the GARCH recursion, either current or lagged depending upon the timing.

Code: Select all

all 500
set x = %ran(1.0)
set y = .1*x+%ran(1.0)
*
linreg x / ux
# constant x{1 2} y{1 2}
frml(lastreg,vector=bx) xf
*
linreg y / uy
# constant x{0 1} y{1 2}
frml(lastreg,vector=by) yf
*
vcv
# ux uy
*
dec series[symm] hh
gset hh = %sigma
set uux = %sigma(1,1)
set uuy = %sigma(2,2)
set hx  = %sigma(1,1)
set hy  = %sigma(2,2)
compute rho = %cvtocorr(%sigma)(1,2)
*
dec vect gx(4) gy(4)
*
frml hxf = gx(1)+gx(2)*hx{1}+gx(3)*uux{1}+gx(4)*uuy{1}
frml hyf = gy(1)+gy(2)*hy{1}+gy(3)*uux{0}+gy(4)*uuy{1}
*
compute gx(1)=%sigma(1,1)*(1-.2-.6),gx(2)=.6,gx(3)=.2,gx(4)=.0
compute gy(1)=%sigma(2,2)*(1-.2-.6),gy(2)=.6,gy(3)=.0,gy(4)=.2
*
frml logl = ux=x-xf,uux=ux^2,uy=y-yf,uuy=uy^2,$
   hh(t)(1,1)=hxf,hh(t)(2,2)=hyf,hh(t)(1,2)=rho*sqrt(hh(t)(1,1)*hh(t)(2,2)),$
   %logdensity(hh,||ux,uy||)
*
nonlin(parmset=meanparms) bx by
nonlin(parmset=garchparms) gx gy rho
*
maximize(parmset=meanparms+garchparms) logl