Regression‐type models for extremal dependence

Abstract

We propose a vector generalized additive modeling framework for taking into account the effect of covariates on angular density functions in a multivariate extreme value context. The proposed methods are tailored for settings where the dependence between extreme values may change according to covariates. We devise a maximum penalized log‐likelihood estimator, discuss details of the estimation procedure, and derive its consistency and asymptotic normality. The simulation study suggests that the proposed methods perform well in a wealth of simulation scenarios by accurately recovering the true covariate‐adjusted angular density. Our empirical analysis reveals relevant dynamics of the dependence between extreme air temperatures in two alpine resorts during the winter season.

Modelling non-stationarity in asymptotically independent extremes

“…Relatively little consideration has been given to this problem in the literature, and most of the approaches that do exist rely on the multivariate regular variation framework, thereby being restricted to asymptotically dependent data. For example, Mhalla et al (2019a) and Mhalla et al (2019b) propose semi-parametric models to capture trends in parameters of quantities related to the spectral measure, while de Carvalho and Davison (2014) and Castro-Camilo et al (2018) propose flexible modelling techniques for capturing non-stationary trends in the spectral measure under covariate influence. Mhalla et al (2019) also propose a technique for data exhibiting asymptotic independence, using GAMs to capture trends in the non-stationary extension to the ADF defined in equation (3.1).…”

Conditional marginal expected shortfall

“…As a final comment, observe that in view of assumption pRq, our key statistic T n py 1 , y 2 |x 0 q can be linked to the estimation of Rpy 1 , y 2 |x 0 q, though this is not the objective of the present paper. For what concerns the estimation of the conditional extremal dependence structure, we refer to de Carvalho (2016), Escobar-Bach et al (2018a, b), Castro et al (2018) and Mhalla et al (2019).…”

Tracking change-points in multivariate extremes

“…Statistical models for nonstationary multivariate extremes have only very recently been devised (de Carvalho, 2016;Mhalla et al, 2017;Escobar-Bach et al, 2018;Castro et al, 2018;Gong and Huser, 2019;Mhalla et al, 2019). In particular, Gong and Huser (2019) investigated the dynamics of the extreme dependence between the crypto-currencies Bitcoin and Ethereum and noticed that it has been significantly becoming stronger over the years, thus highlighting the need for a non-stationary analysis.…”