DCC Multivariate GARCH estimation

Question

I'm using 3 stocks (GSPC, STOXX50E and NIKKEI) in order to try to estimate a DCC Garch model.

Usual steps: get the returns of the series, start with a univariate GARCH model and replicate it (...)

Everything seems to work well until I get to the stage that my dccfit() retrieves me an output "incomplete". I need, in the end, to get estimates enough to build 6 equations (one equation for the variance of GSPC, for the variance of STOXX50E , for the variance of NIKKEI, for covariance between GSPC and STOXX50E , for covariance between STOXX50E and NIKKEI and covariance between GSPC and NIKKEI ). Please see my outputs below:

After using print(dccfit), the output is ar1, ma1, omega, alpha1, beta1 for each time series. And in the end joint dcca1 and also joint dccb1.

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Where are the other estimates for me to put in the equation? It seems that I can only estimate a univariate model...

1. What these estimates (alpha,omega,...) stand for? Variance? Mean?... If so, isn't it only a univariate estimation?

2. And the jointdcca1 and jointdccb1? Are they relevant for any equation?

Thanks a lot in advance for your attention.

Answer 1

The DCC model is a 2-step estimation procedure (2-step QMLE).

In the first step, you fit univariate models.

The alpha, omega etc. that you mentioned in your Question 1. are these parameter estimates.

In the second step, you estimate the additional parameters a,b of the matrix Q_t, derived from the decomposition of the conditional correlation matrix R_t, which in turn was obtained by the decomposition of H_t = D_t R_t D_t.