Moderately Heavy Extreme Values under Extreme Long Range Dependence

TL;DR

This paper investigates the behavior of extreme values in strongly dependent stationary sequences with subexponential tails, revealing complex clustering and fractal features through new extremal limit theorems.

Contribution

It introduces functional extremal limit theorems for sequences with extreme long-range dependence, extending understanding beyond classical Gumbel domain results.

Findings

Extreme values form clusters with fractal characteristics

Limit theorems involve non-Gumbel limit objects

Dependence causes multiple large values to influence extremes

Abstract

We consider stationary sequences whose marginal tail is subexponential and lies in the Gumbel Maximum domain of attraction. Due to the extremely strong dependence, their extreme values are caused by multiple big values and are clustered in the large scale with fractal features. We establish functional extremal limit theorems with non-Gumbel limit objects to characterize these delicate phenomena.