Nonlinearities and regimes in conditional correlations with different dynamics

New parameterizations of the dynamic conditional correlation (DCC) model and of the regime-switching dynamic correlation (RSDC) model are introduced, such that these models provide a specific dynamics for each correlation. They imply a non- linear autoregressive form of dependence on lagged correlations and are based on properties of the Hadamard exponential matrix. The new models are applied to a data set of twenty stock market indices, comparing them to the classical DCC and RSDC models. The empirical results show that the new models improve their clas- sical versions in terms of several criteria.