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This paper describes limiting behaviour of tail empirical process associatedwith long memory stochastic volatility models. We show that such process hasdichotomous behaviour, according to an interplay between a Hurst parameter anda tail index. In particular, the limit may be non-Gaussian and/or degenerate,indicating an influence of long memory. On the other hand, tail empiricalprocess with random levels never suffers from long memory. This is verydesirable from a practical point of view, since such the process may be used toconstruct Hill estimator of the tail index. To prove our results we need toestablish several new results for regularly varying distribution functions,which may be of independent interest.

The tail empirical process for some long memory sequences