Extreme quantile estimation for β-mixing time series and applications

Valérie Chavez-Demoulin (1) , Armelle Guillou (2)

1 UNIL - Université de Lausanne = University of Lausanne
2 IRMA - Institut de Recherche Mathématique Avancée

In this paper, we discuss the application of extreme value theory in the context of stationary β-mixing sequences that belong to the Fréchet domain of attraction. In particular, we propose a methodology to construct bias-corrected tail estimators. Our approach is based on the combination of two estimators for the extreme value index to cancel the bias. The resulting estimator is used to estimate an extreme quantile. In a simulation study, we outline the performance of our proposals that we compare to alternative estimators recently introduced in the literature. Also, we compute the asymptotic variance in specific examples when possible. Our methodology is applied to two datasets on finance and environment.

Mots clés: Asymptotic normality; β-mixing; Extreme value index; GARCH models; High quantile; Market index; Return level; Value-at-Risk; Wind speed data

Domaines: Statistiques [math.ST]

Valérie Chavez-Demoulin, Armelle Guillou. Extreme quantile estimation for β-mixing time series and applications. Insurance: Mathematics and Economics, 2018, 83, pp.59-74. ⟨10.1016/j.insmatheco.2018.09.004⟩. ⟨hal-02392748⟩