Analytic Moments For Conditional And Aggregated GARCH Variances And Returns

Knowledge of the dynamic properties and the higher moments of the distribution of returns on financial

assets is of particular importance, since these processes exhibit volatility clustering and their distributions are

also known to be non-normal. Thus the forecasting ability of GARCH models, which capture both of these

effects, has been the subject of numerous research papers in the financial econometrics literature. However,

most papers consider only the point variance forecasts generated by a GARCH process. This paper shows

how approximate predictive distributions for forward and cumulative future returns and variances, in a

generic asymmetric GARCH model, can be constructed. These are based on new analytic formulae for the

first four moments, of the conditional returns and conditional variance distributions, and of the aggregated

returns and variances.