Before revision:  we derive analytic expressions for the first four conditional moments of the forward return, of the forward variance, of the aggregated return and of the aggregated variance -- corresponding moments for some specific GARCH models largely used in practice are recovered as special cases ; we derive the limits of these moments as the time horizon increases, establishing regularity conditions for the moments of aggregated returns to converge to normal moments ;
After revision:  we derive analytic expressions for the first four conditional moments of the forward return, of the forward variance, of the aggregated return and of the aggregated variance -- corresponding moments for some specific GARCH models largely used in practice are recovered as special cases . We also the limits of these moments as the time horizon increases, establishing regularity conditions for the moments of aggregated returns to converge to normal moments ;