Contemporaneous aggregation of GARCH processes

In this paper the effect of contemporaneous aggregation of het-erogeneous GARCH processes as the cross-sectional size diverges to infinity is studied. We analyze both cases of cross-sectionally depen-dent 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 aggre-gate volatility is not attainable. We also explore more general forms of cross-sectional dependence and various types of aggregation schemes