A Multivariate GARCH Model with Time-Varying Correlations

In this paper we propose a new multivariate GARCH model with timevarying correlations. We adopt the vech representation based on the conditional variances and the conditional correlations. While each conditional-variance term is assumed to follow a univariate GARCH formulation, the conditional-correlation matrix is postulated to follow an autoregressive moving average type of analogue. By imposing some suitable restrictions on the conditional-correlation-matrix equation, we manage to construct a MGARCH model in which the conditional-correlation matrix is guaranteed to be positive de ̄nite during the optimisation. Thus, our new model retains the intuition and interpretation of the univariate GARCH model and yet satis ̄es the positive-de ̄nite condition as found in the constant-correlation and BEKK models. We report some Monte Carlo results on the ̄nite-sample distributions of the QMLE of the varying-correlation MGARCH model. The new model is applied to some real data sets. It is found that extending the constant-correlation model to allow for time-varying correlations provides some interesting time histories that are not available in a constant-correlation model.