The tail empirical process for long memory stochastic volatility sequences

This paper describes the limiting behaviour of tail empirical processes associated with long memory stochastic volatility models We show that such a process has dichotomous behaviour, according to an interplay between the Hurst parameter and the tail index On the other hand the tail empirical process with random levels never suffers from long memory This is very desirable from a practical point of view since such a process may be, used to construct the Hill estimator of the tall index To prove our results we need to establish new results for regularly varying distributions which may be of Independent interest (c) 2010 Elsevier B V All rights reserved