Time-varying extreme value dependence with application to leading European stock markets

Castro‐Camilo, Daniela; Carvalho, Miguel de; Wadsworth, Jennifer L.

doi:10.1214/17-aoas1089

Cited by 29 publications

(14 citation statements)

References 59 publications

(62 reference statements)

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“…Therefore, any localized version of nonparametric estimators of the spectral measure will require large data sets to perform well. A localized estimator of the so-called Pickands dependence function, which describes the spectral measure after a suitable marginal standardization, has been analyzed by Escobar-Bach et al (2018) in a general setting, while Castro-Camilo et al (2018) used a kernel based estimator of a parametric density of the spectral measure; see also Hoga (2021) for tests of a changing tail dependence in a parametric time series setting.…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference on a Changing Extremal Dependence Structure

Drees¹

2022

Preprint

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We analyze the extreme value dependence of independent, not necessarily identically distributed multivariate regularly varying random vectors. More specifically, we propose estimators of the spectral measure locally at some time point and of the spectral measures integrated over time. The uniform asymptotic normality of these estimators is proved under suitable nonparametric smoothness and regularity assumptions. We then use the process convergence of the integrated spectral measure to devise consistent tests for the null hypothesis that the spectral measure does not change over time.

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Section: Introductionmentioning

confidence: 99%

Statistical Inference on a Changing Extremal Dependence Structure

Drees¹

2022

Preprint

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“…Promising extreme value approaches are emerging that model non-stationarity within the dependence as a function of covariates (Huser and Genton 2016;Castro-Camilo et al 2018. However, these methods are mathematically and computationally complex.…”

Section: Introductionmentioning

confidence: 99%

A regionalisation approach for rainfall based on extremal dependence

2020

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To mitigate the risk posed by extreme rainfall events, we require statistical models that reliably capture extremes in continuous space with dependence. However, assuming a stationary dependence structure in such models is often erroneous, particularly over large geographical domains. Furthermore, there are limitations on the ability to fit existing models, such as max-stable processes, to a large number of locations. To address these modelling challenges, we present a regionalisation method that partitions stations into regions of similar extremal dependence using clustering. To demonstrate our regionalisation approach, we consider a study region of Australia and discuss the results with respect to known climate and topographic features. To visualise and evaluate the effectiveness of the partitioning, we fit max-stable models to each of the regions. This work serves as a prelude to how one might consider undertaking a project where spatial dependence is non-stationary and is modelled on a large geographical scale.

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“…de Carvalho () advocated the use of covariate‐adjusted angular densities, and Escobar‐Bach, Goegebeur, and Guillou () discussed estimation—in the bivariate and covariate‐dependent framework—of the Pickands dependence function based on local estimation with a minimum density power divergence criterion. Recently, Mhalla, Chavez‐demoulin, and Naveau () have constructed in a nonparametric framework smooth models for predictor‐dependent Pickands dependence functions based on generalized additive models, whereas Castro‐Camillo, de Carvalho, and Wadsworth () proposed nonparametric regression methods for predictor‐dependent angular measures; a key advantage of our method is that it can be used for modeling a high number (with limitation given by the sample size) of covariates of any type (from categorical to continuous), and it combines the flexibility of GAM along with a parametric specification to effectively learn about the dynamics governing the extremal dependence structure.…”

Section: Introductionmentioning

confidence: 99%

Regression‐type models for extremal dependence

Mhalla

Carvalho

Chavez‐Demoulin

2019

Scandinavian J Statistics

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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.

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Time-varying extreme value dependence with application to leading European stock markets

Cited by 29 publications

References 59 publications

Statistical Inference on a Changing Extremal Dependence Structure

Statistical Inference on a Changing Extremal Dependence Structure

A regionalisation approach for rainfall based on extremal dependence

Regression‐type models for extremal dependence

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