Contemporaneous aggregation of GARCH processes

In this article, the effect of contemporaneous aggregation of heterogeneous generalized autoregressive conditionally heteroskedastic (GARCH) processes, as the cross-sectional size diverges to infinity is studied. We analyse both cases of cross-sectionally dependent and independent individual processes. The limit aggregate does not belong to the class of GARCH processes. Dynamic conditional heteroskedasticity is only preserved when the individual processes are sufficiently cross-correlated, although long memory for the limit aggregate volatility is not attainable. We also explore more general forms of cross-sectional dependence and various types of aggregation schemes.