Forecasting the conditional covariance matrix using DCC-GARCH

In this recipe, we cover an extension of the CCC-GARCH model: Engle's Dynamic Conditional Correlation GARCH (DCC-GARCH) model. The main difference between the two is that in the latter, the conditional correlation matrix is not constant over time—we have R_t instead of R.

There are some nuances in terms of estimation, but the outline is similar to the CCC-GARCH model:

• Estimate the univariate GARCH models for conditional volatility
• Estimate the DCC model for conditional correlations

In the second step of estimating the DCC model, we use a new matrix Q_t, representing a proxy correlation process.

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The first equation describes the relationship between the conditional correlation matrix R_t and the proxy process Q_t. The second equation represents the dynamics of the proxy process. The last equation shows...