Structured Multivariate Volatility Models

This paper proposes structured parametrizations for multivariate volatility models, which use spatial weight matrices induced by economic proximity. These structured speci…cations 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 ‡exible, 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 re‡ects the chosen notion of economic classi…cation; iv) model-estimation computations are faster than for unstructured speci…cations. We give examples of structured speci…cations for multivariate GARCH models as well as for Stochasticand 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. Keywords: MGARCH, Stochastic Volatility, Realized Volatility, Spatial models, ANOVA. J.E.L. Classi…cation: C31, C32, G11. Paper presented at the second ETSERN meeting in Copenhagen, and at CREATES in Århus, November 2008. Partial …nancial support from Italian MUR Grant Co…n2006-13-1140 is gratefully acknowledged. We thank the following people for useful comments on a previous version of the paper: Søren Johansen, Federico Martellosio, Michael McAleer, Christophe Planas, Timo Teräsvirta, as well as several participants to paper presentations.