Before revision:  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 ; and we demonstrate empirically that some excellent approximate predictive distributions can be obtained from these analytic moments, thus precluding the need for time-consuming simulations.
After revision:  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 . Our empirical study yields excellent approximate predictive distributions can be obtained from these analytic moments, thus precluding the need for time-consuming simulations.