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I have already estimated my DCC GARCH parameters and forecasted covariances on a rolling window basis. Now I want to use CCC GARCH forecasted covariances on the same rolling window basis as a threshold. I have two questions regarding the CCC correlation matrix:

  1. I know that the correlation matrix for CCC is supposed to be constant but in a rolling window it should change with each window based on the data in that window right?

  2. What are the practical steps to calculate the CCC one step ahead correlation matrix?

Thanks in advance!

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I know that the correlation matrix for CCC is supposed to be constant but in a rolling window it should change with each window based on the data in that window right?

Yes, that is correct. The correlation matrix will be constant for the window at hand, but not across windows. This is simply because it is estimated independently in each window without restricting it to be the same across windows.

What are the practical steps to calculate the CCC one step ahead correlation matrix?

The forecast equals the in-sample fitted correlation matrix, because it is supposed to stay constant over time.

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  • $\begingroup$ thanks! the insample fitted correlation matrix is simply the covariance of the standardized residuals (Q) divided by the sqrt(Q)*sqrt(Q) right? $\endgroup$ – Hsk May 12 '17 at 10:33
  • $\begingroup$ @Hsk, it should be something like $\text{diag}(Q)^{-0.5} \times Q \times \text{diag}(Q)^{-0.5}$. Can't you see it directly as part of the output of the estimated model? $\endgroup$ – Richard Hardy May 12 '17 at 10:54
  • $\begingroup$ yeah that's what I meant. I was planning on using the quasi correlations from my DCC model after constraining alpha and beta to zero or alternatively just taking the covariance of standardized errors to get Q (using sd of univariate GARCH ofc) Would that be correct? $\endgroup$ – Hsk May 12 '17 at 11:07
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    $\begingroup$ @Hsk, If you are technically able to restrict DCC to turn it into CCC, it will be fine. Just taking the covariance of standardized errors from DCC does not sound right, though. It should be approximately an identity matrix with zero element off the main diagonal. This is quite different from what you need. $\endgroup$ – Richard Hardy May 12 '17 at 11:44
  • $\begingroup$ do you know any alternative way to get the correlation matrix for CCC without restricting DCC? Actually I have used a toolbox for DCC so I realized it won't be easy to restrict it... $\endgroup$ – Hsk May 12 '17 at 11:59

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