Moment and Memory Properties of Linear Conditional Heteroscedasticity Models

This paper analyses moment and near-epoch dependence properties for the general class of models in which the conditional variance is a linear function of squared lags of the process. It is shown how the properties of these processes depend independently on the sum and rate of convergence of the lag coefficients, the former controlling the existence of moments, and the latter the memory of the volatility process. Conditions are derived for existence of second and fourth moments, and also for the processes to be L1and L2near epoch dependent (NED). The geometric convergence cases (GARCH and IGARCH) are compared with models having hyperbolic convergence rates, the FIGARCH, and a newly proposed generalization, the HYGARCH model. The latter models are applied to Asian exchange rates over the 1997 crisis period, and are shown to account well for the characteristics of the data.