BAYESIAN CLUSTERING OF SIMILAR MULTIVARIATE GARCH MODELS

We consider the estimation of a large number of GARCH models, say of the order of several hundreds. Especially in the multivariate case, the number of parameters is extremely large. To reduce this number and render estimation feasible, we regroup the series in a small number of clusters. Within a cluster, the series share the same model and the same parameters. Each cluster should therefore contain similar series. What makes the problem interesting is that we do not know a piori which series belongs to which cluster. The overall model is therefore a finite mixture of distributions, where the weights of the components are unknown parameters and each component distribution has its own conditional mean and variance specification. Inference is done by the Bayesian approach, using data augmentation techniques. Illustrations are provided.