Spatial effects in multivariate ARCH

This paper proposes a new approach for the specification of multivariate GARCH models for data sets with a potentially large cross-section dimension. The approach exploits the spatial dependence structure associated with asset characteristics, like industrial sectors and capitalization size. We use the acronym SEARCH for this model, short for Spatial Effects in ARCH. This parametrization extends current feasible specifications for large scale GARCH models, while keeping the numbers of parameters linear with respect to the number of assets. An application to daily returns on 20 stocks from the NYSE for the period January 1994 to June 2001 shows the benefits of the present specification.