This paper considers Dynamic Conditional Correlations (DCC) GARCH models in which the time-varying coefficients, including the conditional correlation matrix, are functions of the realizations of an exogenous stochastic process. Time series generated by this model are in general nonstationary. Necessary and sufficient conditions are given for the existence of non-explosive solutions, and for the existence of second-order moments of these solutions. Potential applications concern the modeling of the volatility of a vector of energy prices, the model coefficients depending on the weather conditions.
Keywords: Dynamic conditional correlation, Existence of nonexplosive solutions, Multivariate GARCH, Nonstationary processes, Time-varying models