DCC GARCH with exogenous variables

[jessyueh]

Dear all,
I am working on DCC GARCH programming recently.
The RATS 6.2 has provided me an example named “GARCHMVDCC2”.
I’m trying to understand every instruction it uses to estimate my own bivariate GARCH model.

But,
I still got 2 questions that I can’t solve myself.
1) When should we use two-step DCC to estimate our model?
The RATS has provided a multivarate GARCH instruction with DCC option to estimate Engle(2002)’s model. Why should we use two-step DCC? Is there any article I can refer to?
Besides, the last results estimated by "GARCHMVDCC2" are not the same with the one estimated by original RATS 'mv = dcc'.

2) How could I add extra regressors in covariance equation?
The RATS has a ‘xregressors’ option to include my own variables in variance equation, but not the covariance (or correlation) equation. The ‘GARCHMVDCC2’ program has several codes as follows:

**********
nonlin a b
dec frml[symm] qf
frml qf = (qx=(1-a-b)*rr+a*uu{1}+b*q{1})
frml logl = q=qf,%logdensity(%cvtocorr(q),%xt(eps,t))
compute b=.80,a=.10
maximize logl 2 *
*********

Should I add the extra regressors in line 1st and 3rd ? just like:
nonlin a b m
dec frml[symm] qf
frml qf =(qx=(1-a-b)*rr+a*uu{1}+b*q{1}+m*X)
------------
I really appreciate your help.

Sincerely,

A Ph.D. student in Taiwan

[TomDoan]

Dear all,
I am working on DCC GARCH programming recently.
The RATS 6.2 has provided me an example named “GARCHMVDCC2”.
I’m trying to understand every instruction it uses to estimate my own bivariate GARCH model.

But,
I still got 2 questions that I can’t solve myself.
1) When should we use two-step DCC to estimate our model?
The RATS has provided a multivarate GARCH instruction with DCC option to estimate Engle(2002)’s model. Why should we use two-step DCC? Is there any article I can refer to?
Besides, the last results estimated by "GARCHMVDCC2" are not the same with the one estimated by original RATS 'mv = dcc'.

The two-step procedure can be employed when there are so many variables that the more efficient full system estimation is impractical. MV=DCC in GARCH does the full system estimator, not the two-step, so it definitely won't match. There are also slight differences between the handling of initial conditions between the GARCH instruction and the code for using MAXIMIZE.

2) How could I add extra regressors in covariance equation?
The RATS has a ‘xregressors’ option to include my own variables in variance equation, but not the covariance (or correlation) equation. The ‘GARCHMVDCC2’ program has several codes as follows:

**********
nonlin a b
dec frml[symm] qf
frml qf = (qx=(1-a-b)*rr+a*uu{1}+b*q{1})
frml logl = q=qf,%logdensity(%cvtocorr(q),%xt(eps,t))
compute b=.80,a=.10
maximize logl 2 *
*********

Should I add the extra regressors in line 1st and 3rd ? just like:
nonlin a b m
dec frml[symm] qf
frml qf =(qx=(1-a-b)*rr+a*uu{1}+b*q{1}+m*X)
------------
I really appreciate your help.

What is "X"? m*X somehow has to be a symmetric matrix with dimensions N x N (N=number of series).