Measuring Tail Dependence in Linear Processes: Theory and Empirics

TL;DR

This paper introduces a new dependence measure for analyzing joint extreme events in financial time series, especially heavy-tailed and persistent behaviors, supported by simulations and high-frequency cryptocurrency data.

Contribution

It proposes a novel approach to measure tail dependence that accounts for non-identical and identical heavy-tailed distributions in linear processes.

Findings

The new dependence measure captures joint extremes more effectively.

Persistence properties significantly influence tail dependence.

Simulation results validate the proposed methodology.

Abstract

The quantitative analysis of financial time series often reveals two distinct features that standard Gaussian frameworks fail to capture: heavy-tailed marginal distributions and the phenomenon of extreme co-movements.While extreme value theory characterizes marginal behavior, Copulas provide a functional bridge to describe the dependence structure independently of the marginals. We are proposing a different way of looking at the joint extremes on the basis of a dependence measure. The proposed idea incorporates both the non-identical and identical regularly varying distributions. Informed by the analysis of some high-frequency cryptocurrency datasets, the effect of persistence property have been thoroughly studied under these setups. A detailed simulation study confirms our intuition and findings.