 |
To avoid imposing the constraints of a common dynamics on conditional correlations in large dimensions, new versions of the DCC model and of the RSDC model are introduced. These models provide
a specific dynamics to each correlation. They use parameterizations implying a nonlinear autoregressive form of dependence on lagged correlations and are based on properties of the Hadamard
exponential matrix. In their simplest form, the parameterizations proposed for these new models ensure the positive definiteness of the conditional correlation matrix and require the estimation of the
same number of parameters as the corresponding scalar forms of DCC (Engle, 2002; Aielli, 2013) and RSDC (Pelletier, 2006). More flexible versions of the models are also available, with the
introduction of a larger number of parameters, for which a general-to-specific procedure is proposed to identify a more parsimonious model. These new models, called the NonLinear AutoRegressive
Correlation (NLARC) and the Flexible RSDC (FRSDC) models, are applied to a data set of twenty stock market indices, comparing them to the DCC model of Engle (2002) and the RSDC model of
Pelletier (2006). The empirical results show that the new models improve their simpler versions in terms of fit and out-of-sample statistical forecasts.
