Covariance matrix of DCC-GARCH parameter estimates

[Jules89]

Dear Tom,

I have a more conceptual question related to the estimation of DCC-GARCH models. How is the joint covariance matrix of the parameter estimates (given by %xx) determined/estimated?
From my understanding there is a univariate GARCH model for each series in the first step and in the second step the parameters of the joint correlation equation are estimated (including the time invariant Q matrix towards which the DCCs converge, given stationarity). So my question is: given this two-step procedure, how is the joint covariance matrix of the parameters defined?

Best

Jules

[TomDoan]

RATS by default does a full joint likelihood maximization for DCC. There's a GARCHMVDCC2.RPF which does the two-step procedure---it does one iteration with BHHH to get an estimate of the overall covariance matrix. However, if you have 10 or fewer variables, there is no reason to do the two step procedure, which is consistent but less efficient.

[Jules89]

Dear Tom,

I wonder if you could give me a reference on how the full information maximum likelihood estimation of the DCC GARCH model works?

Best

Jules

[TomDoan]

It's either the standard BFGS or BHHH estimate of the covariance matrix, depending upon your estimation options.

[Jules89]

Thanks Tom,

But what I actually meant was a reference related to the derivation of the one step likelihood itself.
Is this written down in the original paper? I am struggling to find a comprehensive summary of the formulas, as everywhere solely the two step approach is described.

Thank you very much

Best

Jules

[TomDoan]

The full sample likelihood is in the original DCC paper.