No. 449 - Contemporaneous aggregation of GARCH processes

In this paper we study the effect of contemporaneous aggregation of heterogeneous GARCH processes as the cross-sectional size diverges to infinity. A complete statistical characterization of the limit aggregate is provided under general assumptions on the form and degree of heterogeneity of the micro GARCH processes. Implications on the memory and on modelling issues of the limit portfolios are also developed. The key features which characterize the results are the shape of the cross-sectional distribution of micro parameters, their degree of cross-sectional dependence and the degree of cross-sectional dependence of the rescaled innovations. These features provide a set of testable implications with respect to the relationship between the micro and aggregate statistical properties.