Many parameterizations have been introduced to model covariance dynamics. Yet estimating even moderately large models without excessive parameter restrictions, typically through parameter pooling, remains a formidable challenge. Most specifications suffer from a number of issues as the dimension increases, including difficultiesensuring uniformly positive-definite conditional covariances, numerous parameters needing to be simultaneously estimated or many non-linear constraints. This paper examines the classes of models capable of estimating conditional covariances when the cross-section dimension is large, including factor GARCH specifications, restricted vector GARCH processes, dynamic correlation GARCH models and proposes feasible asymmetric extensions for each. Large dimension problems also present difficulties for specification testing. Using up to 50 assets, we evaluate the performance of these specifications out-of-sample employing statistical and economically meaningful criteria against two benchmark models: an exponential smoother and a simple but empirically successful moving average factor model. We find there is value in modeling time-varying covariances, although tightly parameterized models generally perform better when evaluated with economically meaningful criteria.
Stored only when both papers are in the corpus — 54 citations exist upstream.