Heavy tailed time series with extremal independence

TL;DR

This paper studies heavy tailed stationary time series with extremal independence, introducing new tools like scaling functions and exponents to better understand their joint extreme behavior beyond traditional tail dependence measures.

Contribution

It introduces a novel framework using scaling functions and exponents to analyze extremal independence in heavy tailed time series, extending beyond classical methods.

Findings

Derived explicit scaling functions for various models

Calculated scaling exponents for Markov and autoregressive models

Provided insights into joint extremes in extremally independent series

Abstract

We consider strictly stationary heavy tailed time series whose finite-dimensional exponent measures are concentrated on axes, and hence their extremal properties cannot be tackled using classical multivariate regular variation that is suitable for time series with extremal dependence. We recover relevant information about limiting behavior of time series with extremal independence by introducing a sequence of scaling functions and conditional scaling exponent. Both quantities provide more information about joint extremes than a widely used tail dependence coefficient. We calculate the scaling functions and the scaling exponent for variety of models, including Markov chains, exponential autoregressive model, stochastic volatility with heavy tailed innovations or volatility.