EXTREME CONDITIONAL EXPECTILE ESTIMATION IN HEAVY-TAILED HETEROSCEDASTIC REGRESSION MODELS

Expectiles define a least squares analogue of quantiles. They have been the focus of a substantial quantity of research in the context of actuarial and financial risk assessment over the last decade. The behaviour and estimation of unconditional extreme expectiles using independent and identically distributed heavy-tailed observations have been investigated in a recent series of papers. We build here a general theory for the estimation of extreme conditional expectiles in heteroscedastic regression models with heavy-tailed noise; our approach is supported by general results of independent interest on residual-based extreme value estimators in heavy-tailed regression models, and is intended to cope with covariates having a large but fixed dimension. We demonstrate how our results can be applied to a wide class of important examples, among which are linear models, single-index models as well as ARMA and GARCH time series models. Our estimators are showcased on a numerical simulation study and on real sets of actuarial and financial data.

Automated summary

Expectiles are a least squares analogue of quantiles that have been extensively researched in the fields of actuarial and financial risk assessment over the past decade. Recent papers have focused on the estimation of unconditional extreme expectiles using heavy-tailed observations. The general theory proposed in this study aims to estimate extreme conditional expectiles in heteroscedastic regression models with heavy-tailed noise, with a focus on dealing with high-dimensional covariates. The approach is demonstrated through various examples, including linear models and time series models like ARMA and GARCH.