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...

This paper examines volatility in UK Long Gilt and Short Sterling futures over several intra-day frequencies. Initial GARCH model estimates are found to exhibit remaining residual structure and to be inconsistent with theoretical temporal aggregation results for all frequencies other than the...

This paper considers the moments of a family of first-order GARCH processes. First, a general condition of the existence of any integer moment of the absolute values of the observations is given. Second, a general expression for this moment as a function of lower-order moments is derived. Third,...

In this paper, a necessary and sufficient condition for the existence of the unconditional fourth moment of the GARCH (p, q) process is given as well as an expression for the moment itself. Furthermore, the autocorrelation function of the centred and squared observations of this process is...

Recent empirical work indicates that, in a variety of financial markets, both conditional expectations and conditional variances of asset returns are time-varying. The purpose of this paper is to determine whether these joint fluctuations of conditional first and second moments are consistent...