scholarly journals Local Estimation of the Conditional Stable Tail Dependence Function

2018 ◽  
Vol 45 (3) ◽  
pp. 590-617 ◽  
Author(s):  
Mikael Escobar-Bach ◽  
Yuri Goegebeur ◽  
Armelle Guillou
Keyword(s):  
Tail Dependence ◽  
Dependence Function ◽  
Local Estimation ◽  
Stable Tail Dependence Function

Equivalent representations of max-stable processes via ℓp-norms

2018 ◽  
Vol 55 (1) ◽  
pp. 54-68
Author(s):  
Marco Oesting
Keyword(s):  
Spectral Representation ◽  
Stable Process ◽  
Tail Dependence ◽  
Stable Processes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Dependence Function ◽  
Special Cases ◽  
Necessary And Sufficient ◽  
Stable Tail Dependence Function

Abstract While max-stable processes are typically written as pointwise maxima over an infinite number of stochastic processes, in this paper, we consider a family of representations based on ℓp-norms. This family includes both the construction of the Reich–Shaby model and the classical spectral representation by de Haan (1984) as special cases. As the representation of a max-stable process is not unique, we present formulae to switch between different equivalent representations. We further provide a necessary and sufficient condition for the existence of an ℓp-norm-based representation in terms of the stable tail dependence function of a max-stable process. Finally, we discuss several properties of the represented processes such as ergodicity or mixing.

scholarly journals Bias-corrected estimation of stable tail dependence function

2016 ◽  
Vol 143 ◽  
pp. 453-466 ◽  
Author(s):  
Jan Beirlant ◽  
Mikael Escobar-Bach ◽  
Yuri Goegebeur ◽  
Armelle Guillou
Keyword(s):  
Tail Dependence ◽  
Dependence Function ◽  
Stable Tail Dependence Function

scholarly journals Bias-corrected and robust estimation of the bivariate stable tail dependence function

Test ◽  
2016 ◽  
Vol 26 (2) ◽  
pp. 284-307 ◽  
Author(s):  
Mikael Escobar-Bach ◽  
Yuri Goegebeur ◽  
Armelle Guillou ◽  
Alexandre You
Keyword(s):  
Robust Estimation ◽  
Tail Dependence ◽  
Dependence Function ◽  
Stable Tail Dependence Function

scholarly journals An estimator of the stable tail dependence function based on the empirical beta copula

Extremes ◽  
2018 ◽  
Vol 21 (4) ◽  
pp. 581-600 ◽  
Author(s):  
Anna Kiriliouk ◽  
Johan Segers ◽  
Laleh Tafakori
Keyword(s):  
Tail Dependence ◽  
Dependence Function ◽  
Stable Tail Dependence Function

scholarly journals On Conditional Value at Risk (CoVaR) for tail-dependent copulas

2017 ◽  
Vol 5 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Piotr Jaworski
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Tail Dependence ◽  
Extreme Value ◽  
Conditional Value At Risk ◽  
Dependence Function ◽  
Conditioning Event

Abstract The paper deals with Conditional Value at Risk (CoVaR) for copulas with nontrivial tail dependence. We show that both in the standard and the modified settings, the tail dependence function determines the limiting properties of CoVaR as the conditioning event becomes more extreme. The results are illustrated with examples using the extreme value, conic and truncation invariant families of bivariate tail-dependent copulas.

scholarly journals Tail Dependence for Regularly Varying Time Series

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Ai-Ju Shi ◽  
Jin-Guan Lin
Keyword(s):  
Time Series ◽  
Conditional Probability ◽  
Tail Dependence ◽  
Intensity Measure ◽  
Dependence Function ◽  
Regularly Varying

We use tail dependence functions to study tail dependence for regularly varying (RV) time series. First, tail dependence functions about RV time series are deduced through the intensity measure. Then, the relation between the tail dependence function and the intensity measure is established: they are biuniquely determined. Finally, we obtain the expressions of the tail dependence parameters based on the expectation of the RV components of the time series. These expressions are coincided with those obtained by the conditional probability. Some simulation examples are demonstrated to verify the results we established in this paper.

scholarly journals On Truncation Invariant Copulas and their Estimation

2017 ◽  
Vol 5 (1) ◽  
pp. 133-144
Author(s):  
Piotr Jaworski
Keyword(s):  
Tail Dependence ◽  
Functional Parameter ◽  
Linear Estimator ◽  
Left Truncation ◽  
Lower Tail ◽  
Dependence Function ◽  
The Family

AbstractThe paper deals with the family of irreducible left truncation invariant bivariate copulas, which admit a nontrivial lower tail dependence function. Such copulas, similarly as the Archimedean ones, are characterized by a functional parameter, a generator being an increasing convex function.We provide a nonparametric, piece-wise linear estimator of such generators.

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