Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model
分析条件方差为滞后平方线性函数的条件异方差模型（如GARCH、IGARCH、FIGARCH及新提出的HYGARCH）的二阶和四阶矩存在条件及近邻依赖的有限记忆条件，并将HYGARCH模型应用于10种日度美元汇率及1997年危机期间的亚洲汇率数据，发现该模型在危机前后具有显著稳定性。
This article analyses the statistical properties of that general class of conditional heteroscedasticity models in which the conditional variance is a linear function of squared lags of the process. GARCH, IGARCH, FIGARCH, and a newly proposed generalization, the HYGARCH model, belong to this class. Conditions are derived for the existence of second and fourth moments, and for the limited memory condition of near-epoch dependence. The HYGARCH model is applied to 10 daily dollar exchange rates, and also to data for Asian exchange rates over the 1997 crisis period. In the latter case, the model exhibits notable stability across the pre-crisis and post-crisis periods.