Statistical inference for heavy tailed series with extremal independence

TL;DR

This paper studies statistical methods for analyzing heavy-tailed, extremally independent time series, focusing on estimating normalization factors and limiting distributions under certain asymptotic conditions.

Contribution

It introduces new estimation techniques for normalization and limiting distributions in heavy-tailed, extremally independent time series.

Findings

Estimation procedures for normalization factors are developed.

Limiting distributions are characterized under extremal independence.

The methods are applicable to a broad class of heavy-tailed time series.

Abstract

We consider stationary time series $\{X_j, j \in Z\} whose finite dimensional distributions are regularly varying with extremal independence. We assume that for each $h \geq 1$, conditionally on $X_0$ to exceed a threshold tending to infinity, the conditional distribution of $X_h$ suitably normalized converges weakly to a non degenerate distribution. We consider in this paper the estimation of the normalization and of the limiting distribution.