Log In Sign Up

Extreme expectile estimation for heavy-tailed time series

by   Simone A. Padoan, et al.

Expectiles define a least squares analogue of quantiles. They have lately received substantial attention in actuarial and financial risk management contexts. Unlike quantiles, expectiles define coherent risk measures and are determined by tail expectations rather than tail probabilities; unlike the popular Expected Shortfall, they define elicitable risk measures. This has motivated the study of the behaviour and estimation of extreme expectiles in some of the recent statistical literature. The case of stationary but weakly dependent observations has, however, been left largely untouched, even though correctly accounting for the uncertainty present in typical financial applications requires the consideration of dependent data. We investigate here the theoretical and practical behaviour of two classes of extreme expectile estimators in a strictly stationary β-mixing context, containing the classes of ARMA, ARCH and GARCH models with heavy-tailed innovations that are of interest in financial applications. We put a particular emphasis on the construction of asymptotic confidence intervals adapted to the dependence framework, whose performance we contrast with that of the naive intervals obtained from the theory of independent and identically distributed data. The methods are showcased in a numerical simulation study and on real financial data.


page 1

page 2

page 3

page 4


Joint inference on extreme expectiles for multivariate heavy-tailed distributions

The notion of expectiles, originally introduced in the context of testin...

Estimation of conditional extreme risk measures from heavy-tailed elliptical random vectors

In this work, we focus on some conditional extreme risk measures estimat...

Extreme expectile estimation for short-tailed data

The use of expectiles in risk management contexts has recently gathered ...

Change-Point Testing and Estimation for Risk Measures in Time Series

We investigate methods of change-point testing and confidence interval c...

Spliced Binned-Pareto Distribution for Robust Modeling of Heavy-tailed Time Series

This work proposes a novel method to robustly and accurately model time ...

Latent Model Extreme Value Index Estimation

We propose a novel strategy for multivariate extreme value index estimat...

Certain characteristics of financial management strategies of people living in extreme poverty

This study presents the structure of financial management of incomes, ex...