Moderately Heavy Extreme Values under Extreme Long Range Dependence
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.
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