The tail empirical process for some long memory sequences

Details The tail empirical process for some long memory sequences The tail empirical process for some long memory sequences

2010-01-17

arxiv.org/abs/1001.2916v2

Stochastic Processes and their Applications 121, 1 (2011) 109-134

Mathematics

Statistics Theory

Scientific paper

10.1016/j.spa.2010.09.001

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

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