In this paper we consider a general first-order power ARCH process and, in particular, a special case in which the power parameter approaches zero. These considerations give us the autocorrelation function of the logarithms of the squared observations for first-order exponential and logarithmic...

In this paper we consider the fourth moment structure of a class of first-order Exponential GARCH models. This class contains as special cases both the standard Exponential GARCH model and the symmetric and asymmetric Logarithmic GARCH one. Conditions for the existence of any arbitrary moment...