Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model

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), and also to be L0-approximable, in the absence of moments. 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 model is applied to 10 daily dollar exchange rates for 1980-1996, with very similar results. When nested in the HYGARCH framework, the FIGARCH model appears as a valid simplification. However, when applied to data for Asian exchange rates over the 1997 crisis period, a distinctively different pattern emerges. The model exhibits remarkable parameter stability across the preand post-crisis periods.