Copulae in High Dimensions: An Introduction

Okhrin, Ostap; Ristig, Alexander; Xu, Yafei

doi:10.1007/978-3-662-54486-0_13

Cited by 14 publications

(15 citation statements)

References 57 publications

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“…One key advantage of the approach is that it can separate the dependence structure from the marginal distributions 35,36 . Among the different classes of copulas, elliptical copulas offer convenience in model construction and computation of high dimensional problems and have close relation to the classical multivariate method 37,38 . We apply the Gaussian and Student-t copulas which are the most widely used elliptical copulas.…”

Section: Methodsmentioning

confidence: 99%

Biases in national and continental flood risk assessments by ignoring spatial dependence

Metin

Alfieri

Vorogushyn

et al. 2020

Sci Rep

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Recently, flood risk assessments have been extended to national and continental scales. Most of these assessments assume homogeneous scenarios, i.e. the regional risk estimate is obtained by summing up the local estimates, whereas each local damage value has the same probability of exceedance. This homogeneity assumption ignores the spatial variability in the flood generation processes. Here, we develop a multi-site, extreme value statistical model for 379 catchments across Europe, generate synthetic flood time series which consider the spatial correlation between flood peaks in all catchments, and compute corresponding economic damages. We find that the homogeneity assumption overestimates the 200-year flood damage, a benchmark indicator for the insurance industry, by 139%, 188% and 246% for the United Kingdom (UK), Germany and Europe, respectively. Our study demonstrates the importance of considering the spatial dependence patterns, particularly of extremes, in large-scale risk assessments.

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Section: Methodsmentioning

confidence: 99%

Biases in national and continental flood risk assessments by ignoring spatial dependence

Metin

Alfieri

Vorogushyn

et al. 2020

Sci Rep

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“…Now discuss the uniqueness of the maximum in (15). Assume that there exists a pair {i , j } ⊂ I such that i ∉ {i, j} and…”

Section: (λ(D + )) ≤ τ(λ(M))mentioning

confidence: 99%

“…87]. Such a construction, on the one hand, allows for constructing copula models outperforming other recently popular multivariate copula models, e.g., see [15], where HACs are compared to pair and factor copulas in an empirical study from risk management. On the other hand, such a construction involves an extra e ort when estimating HACs, since the structure of a HAC, which represents the way the ACs in this HAC are nested into each other, has to be estimated as another parameter.…”

Section: Introductionmentioning

confidence: 99%

Kendall’s tau and agglomerative clustering for structure determination of hierarchical Archimedean copulas

Górecki

Hofert

Holeňa

2017

Dependence Modeling

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Several successful approaches to structure determination of hierarchical Archimedean copulas (HACs) proposed in the literature rely on agglomerative clustering and Kendall's correlation coe cient. However, there has not been presented any theoretical proof justifying such approaches. This work lls this gap and introduces a theorem showing that, given the matrix of the pairwise Kendall correlation coe cients corresponding to a HAC, its structure can be recovered by an agglomerative clustering technique.

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“…Perhaps the most fundamental finding for copulas is the theorem given by Sklar in [7], which mentions that any multidimensional joint distribution could be obtained via onedimensional marginal distribution functions along with a copula function that shows the structure of dependency among several variables. These distributions were first introduced in the 1940s, and their related machinery and terminology were improved in the 1950s and 1960s [8].…”

Section: Introductionmentioning

confidence: 99%

Revisiting the Copula-Based Trading Method Using the Laplace Marginal Distribution Function

2022

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Pairs trading under the copula approach is revisited in this paper. It is well known that financial returns arising from indices in markets may not follow the features of normal distribution and may exhibit asymmetry or fatter tails, in particular. Due to this, the Laplace distribution is employed in this work to fit the marginal distribution function, which will then be employed in a copula function. In fact, a multivariate copula function is constructed on two indices (based on the Laplace marginal distribution), enabling us to obtain the associated probabilities required for the process of pairs trade and creating an efficient tool for trading.

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Copulae in High Dimensions: An Introduction

Cited by 14 publications

References 57 publications

Biases in national and continental flood risk assessments by ignoring spatial dependence

Biases in national and continental flood risk assessments by ignoring spatial dependence

Kendall’s tau and agglomerative clustering for structure determination of hierarchical Archimedean copulas

Revisiting the Copula-Based Trading Method Using the Laplace Marginal Distribution Function

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