Tail risk inference via expectiles in heavy-tailed time series

2020/04/08 by A. C. Davison, Davison, Anthony C., Simone A. Padoan +3 · 4 citations
Economics, Econometrics and Finance · Mathematics · #60G70 #62G20 #62G32 #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2004.04078

openalex publication_date 2020/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Expectiles define the only law-invariant, coherent and elicitable risk measure apart from the expectation. The popularity of expectile-based risk measures is steadily growing and their properties have been studied for independent data, but further results are needed to use extreme expectiles with dependent time series such as financial data. In this paper we establish a basis for inference on extreme expectiles and expectile-based marginal expected shortfall in a general β-mixing context that encompasses ARMA, ARCH and GARCH models with heavy-tailed innovations. Simulations and applications to financial returns show that the new estimators and confidence intervals greatly improve on existing ones when the data are dependent.

Cited by

• Extreme-PLS with missing data under weak dependence
• Accurate Bayesian inference for tail risk extrapolation in time series
• Non-Parametric Simulation of Multivariate Extreme Events via Spectral Bootstrap
• Asymptotic theory for the likelihood-based block maxima method in time series

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