Detecting breaks in the dependence of multivariate extreme-value distributions

Bücher, Axel; Kinsvater, Paul; Kojadinovic, Ivan

doi:10.1007/s10687-016-0268-y

Cited by 4 publications

(3 citation statements)

References 33 publications

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“…Under the assumption of serial independence, these authors also provide asymptotic theory, which was recently extended in de Haan and Zhou (2021) to trends in the tail index and in Einmahl et al (2022) to multivariate, spatial applications. Finally, change point tests for the tail index and the extremal dependence (i.e., abrupt changes in the tail behavior) can be found in Kojadinovic and Naveau (2017); Bücher et al (2017); Hoga (2017Hoga ( , 2018, with the latter two references explicitly allowing for serially dependent observations.…”

Section: Introductionmentioning

confidence: 99%

Statistics for Heteroscedastic Time Series Extremes

Bücher¹,

Jennessen²

2022

Preprint

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Einmahl, de Haan and Zhou (2016, Journal of the Royal Statistical Society: Series B, 78(1), 31-51) recently introduced a stochastic model that allows for heteroscedasticity of extremes. The model is extended to the situation where the observations are serially dependent, which is crucial for many practical applications. We prove a local limit theorem for a kernel estimator for the scedasis function, and a functional limit theorem for an estimator for the integrated scedasis function. We further prove consistency of a bootstrap scheme that allows to test for the null hypothesis that the extremes are homoscedastic. Finally, we propose an estimator for the extremal index governing the dynamics of the extremes and prove its consistency. All results are illustrated by Monte Carlo simulations. An important intermediate result concerns the sequential tail empirical process under serial dependence.

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Section: Introductionmentioning

confidence: 99%

Statistics for Heteroscedastic Time Series Extremes

Bücher¹,

Jennessen²

2022

Preprint

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“…In a related paper, Quessy (2016) proposed quadratic‐type statistics for testing whether a given collection of induced lower‐dimensional copulas from a multivariate distribution are identical. The

k

‐sample problem for extreme‐value copulas was tackled in Bücher, Kinsvater & Kojadinovic (2017). A similar question arises for conditional dependence structures in multivariate datasets.…”

Section: Introductionmentioning

confidence: 99%

Testing for equality between conditional copulas given discretized conditioning events

2022

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Several procedures have been recently proposed to test the simplifying assumption for conditional copulas. Instead of considering pointwise conditioning events, we study the constancy of the conditional dependence structure when some covariates belong to general Borel conditioning subsets. We introduce several test statistics based on the equality of conditional Kendall's taus and derive their asymptotic distributions under the null hypothesis. In settings where such conditioning events are not fixed ex ante, we propose a data-driven procedure to recursively build such relevant subsets. This procedure is based on decision trees that maximize the differences between the conditional Kendall's taus, which correspond to the leaves of the trees. Empirical results for such tests are illustrated in the Supplementary Material. Moreover, a study of the conditional dependence between financial stock returns is presented and highlights specific contagion effects of past returns. The last application deals with conditional dependence between coverage amounts in an insurance dataset.Résumé: Plusieurs procédures ont été proposées récemment pour tester l'hypothèse simplificatrice pour les copules conditionnelles. Au lieu de considérer des évènements conditionnants ponctuels, nous étudions le caractère constant de la structure de dépendance conditionnelle lorsque certaines covariables appartiennent à des ensembles boréliens conditionnants. Nous introduisons plusieurs statistiques de test basées sur l'égalité des taus de Kendall conditionnels, et nous explicitons leurs distributions asymptotiques sous l'hypothèse nulle. Dans les cas où de tels évènements conditionnants ne sont pas fixés à l'avance, nous proposons une procédure s'appuyant sur les données pour construire récursivement de tels ensembles conditionnants pertinents. Cette procédure est basée sur des arbres de décision qui maximisent les différences entre les taus de Kendall conditionnels, qui correspondent aux feuilles de l'arbre. Les résultats empiriques de ces tests sont présentés dans le contenu supplémentaire. De plus, nous étudions la dépendance conditionnelle entre plusieurs rendements d'actifs et illustrons certains effets particuliers de contagion par les rendements passés. La dernière application traite de la dépendance conditionnelle entre des montants de couverture dans une base de données d'assurance.

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“…For many environmental applications the main interest is in the frequency of hazardous events, e.g., extreme precipitations and floods. Accordingly, there is a number of articles introducing methodology for change-points [Jarušková and Rencová, 2008;Kim and Lee, 2009;Dierckx and Teugels, 2010;Dupuis et al, 2015;Bücher et al, 2015;Kojadinovic and Naveau, 2015] and regression/trend analysis [Chavez-Demoulin and Davison, 2005;Wang and Tsai, 2009;Gardes and Girard, 2010;Dierckx, 2011;Wang et al, 2012;Wang and Li, 2013;Einmahl et al, 2016;de Haan et al, 2015] of extremes, just to name a few recent contributions. For a case study and an overview of many flood trend analyses we refer to Mediero et al [2014].…”

Section: Introductionmentioning

confidence: 99%

Conditional heavy-tail behavior with applications to precipitation and river flow extremes

Kinsvater

Fried

2016

Stoch Environ Res Risk Assess

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This article deals with the right-tail behavior of a response distribution F Y conditional on a regressor vector X " x restricted to the heavy-tailed case of Pareto-type conditional distributions F Y py| xq " P pY ď y| X " xq, with heaviness of the right tail characterized by the conditional extreme value index γpxq ą 0. We particularly focus on testing the hypothesis H 0,tail : γpxq " γ 0 of constant tail behavior for some γ 0 ą 0 and all possible x. When considering x as a time index, the term trend analysis is commonly used. In the recent past several such trend analyses in extreme value data have been published, mostly focusing on time-varying modeling of location and scale parameters of the response distribution. In many such environmental studies a simple test against trend based on Kendall's tau statistic is applied. This test is powerful when the center of the conditional distribution F Y py|xq changes monotonically in x, for instance, in a simple location model µpxq " µ 0`x¨µ1 , x " p1, xq 1 , but the test is rather insensitive against monotonic tail behavior, say, γpxq " η 0`x¨η1 . This has to be considered, since for many environmental applications the main interest is on the tail rather than the center of a distribution. Our work is motivated by this problem and it is our goal to demonstrate the opportunities and the limits of detecting and estimating non-constant conditional heavy-tail behavior with regard to applications from hydrology. We present and compare four different procedures by simulations and illustrate our findings on real data from hydrology: Weekly maxima of hourly precipitation from France and monthly maximal river flows from Germany.

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Detecting breaks in the dependence of multivariate extreme-value distributions

Cited by 4 publications

References 33 publications

Statistics for Heteroscedastic Time Series Extremes

Statistics for Heteroscedastic Time Series Extremes

Testing for equality between conditional copulas given discretized conditioning events

Conditional heavy-tail behavior with applications to precipitation and river flow extremes

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