Structured Multivariate Volatility Models

This paper proposes structured parametrizations for multivariate volatility models, which use spatial weight matrices induced by economic proximity. These structured specifications aim at solving the curse of dimensionality problem, which limits feasibility of model-estimation to small cross-sections for unstructured models. Structured parametrizations possess the following four desirable properties: i) they are flexible, allowing for covariance spill-over; ii) they are parsimonious, being characterized by a number of parameters that grows only linearly with the cross-section dimension; iii) model parameters have a direct economic interpretation that reflects the chosen notion of economic classification; iv) model-estimation computations are faster than for unstructured specifications. We give examples of structured specifications for multivariate GARCH models as well as for Stochastic- and Realized-Volatility models. The paper also discusses how to construct spatial weight matrices that are time-varying and possibly derived from a set of covariates.