MOMENT STRUCTURE OF A FAMILY OF FIRST-ORDER EXPONENTIAL GARCH MODELS
研究了一类一阶指数GARCH模型的矩结构，给出了任意阶矩存在的条件，推导了峰度和绝对值观测正幂自相关的表达式，发现平方误差自相关的衰减率不是常数且初期可能很快。
In this paper we consider the moment structure of a class of first-order exponential generalized autoregressive conditional heteroskedasticity (GARCH) models. This class contains as special cases both the standard exponential GARCH model and the symmetric and asymmetric logarithmic GARCH model. Conditions for the existence of any arbitrary moment are given. Furthermore, the expressions for the kurtosis and the autocorrelations of positive powers of absolute-valued observations are derived. The properties of the autocorrelation structure are discussed and compared to those of the standard first-order GARCH process. In particular, it is seen that, contrary to the standard GARCH case, the decay rate of the autocorrelations of squared errors is not constant and that the rate can be quite rapid in the beginning, depending on the parameters of the model.