Inference on the tail process with application to financial time series modelling

TL;DR

This paper extends nonparametric estimators for extremal dependence in heavy-tailed time series, derives their large-sample distribution, evaluates finite-sample performance, and applies them to financial data to analyze shock persistence.

Contribution

It generalizes spectral tail process estimation to broader stationary series, derives asymptotic distributions, and introduces bootstrap methods for confidence intervals.

Findings

Estimators perform well in finite samples via simulations.

Bootstrap schemes provide reliable confidence intervals.

Application reveals persistence of shocks in stock prices.

Abstract

To draw inference on serial extremal dependence within heavy-tailed Markov chains, Drees, Segers and Warcho{\l} [Extremes (2015) 18, 369--402] proposed nonparametric estimators of the spectral tail process. The methodology can be extended to the more general setting of a stationary, regularly varying time series. The large-sample distribution of the estimators is derived via empirical process theory for cluster functionals. The finite-sample performance of these estimators is evaluated via Monte Carlo simulations. Moreover, two different bootstrap schemes are employed which yield confidence intervals for the pre-asymptotic spectral tail process: the stationary bootstrap and the multiplier block bootstrap. The estimators are applied to stock price data to study the persistence of positive and negative shocks.