Dynamic Conditional Correlation: On properties and estimation

We address some issues that arise with the Dynamic Conditional Correlation (DCC) model. We prove that the DCC large system estimator (DCC estimator) can be inconsistent, and that the traditional interpretation of the DCC correlation parameters can lead to misleading conclusions. We then suggest a more tractable dynamic conditional correlation model (cDCC model). A related large system estimator (cDCC estimator) is described and heuristically proven to be consistent. Sufficient stationarity conditions for cDCC processes of interest, including the covariance-return process, are established. The DCC and cDCC estimators are compared by means of applications to simulated and real data.