Hierarchical Archimedean Copulas for MATLAB and Octave: The HACopula Toolbox

Górecki, Jan; Hofert, Marius; Holeňa, Martin

doi:10.18637/jss.v093.i10

Cited by 10 publications

(2 citation statements)

References 16 publications

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“…For other copula classes and copula applications there is, e.g., a copula package, which provides MATLAB code for time-varying copulas [10] and the HACopula toolbox [11], which implements Hierarchical Archimedean Copulas in MATLAB. The purpose of the MATVines package is to complement the latter by providing code for vine copulas solely written in MATLAB.…”

Section: Motivation and Significancementioning

confidence: 99%

MATVines: A vine copula package for MATLAB

Coblenz¹

2021

SoftwareX

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Section: Motivation and Significancementioning

confidence: 99%

MATVines: A vine copula package for MATLAB

Coblenz¹

2021

SoftwareX

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“…under β 1 = 1, can be fully translated to know-how of sampling its non-OP transformed version, i.e., to LS −1 [( ψ12 ) V1 ], which is known for many families; see the third column of Table 2.3 in Hofert (2010). Also note that free implementations of sampling algorithms for LS −1 [( ψ12 ) V1 ] are available, e.g., in the R package copula (Hofert, Kojadinovic, Maechler and Yan, 2017) or in the HACopula toolbox for MATLAB and Octave (Górecki, Hofert and Holeňa, 2017a).…”

Section: Know-how Of Sampling Lsmentioning

confidence: 99%

Outer power transformations of hierarchical Archimedean copulas: Construction, sampling and estimation

Górecki¹,

Hofert²,

Okhrin³

2020

Preprint

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A large number of commonly used parametric Archimedean copula (AC) families are restricted to a single parameter, connected to a concordance measure such as Kendall's tau. This often leads to poor statistical fits, particularly in the joint tails, and can sometimes even limit the ability to model concordance or tail dependence mathematically. This work suggests outer power (OP) transformations of Archimedean generators to overcome these limitations. The copulas generated by OP-transformed generators can, for example, allow one to capture both a given concordance measure and a tail dependence coefficient simultaneously. For exchangeable OP-transformed ACs, a formula for computing tail dependence coefficients is obtained, as well as two feasible OP AC estimators are proposed and their properties studied by simulation. For hierarchical extensions of OP-transformed ACs, a new construction principle, efficient sampling and parameter estimation are addressed. By simulation, convergence rate and standard errors of the proposed estimator are studied. Excellent tail fitting capabilities of OP-transformed hierarchical AC models are demonstrated in a risk management application. The results show that the OP transformation is able to improve the statistical fit of exchangeable ACs, particularly of those that cannot capture upper tail dependence or strong concordance, as well as the statistical fit of hierarchical ACs, especially in terms of tail dependence and higher dimensions. Given how comparably simple it is to include OP transformations into existing exchangeable and hierarchical AC models, this transformation provides an attractive trade-off between computational effort and statistical improvement.

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Archimedean Copulas

Górecki,

Okhrin

2024

SpringerBriefs in Applied Statistics and Econometrics

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Hierarchical Archimedean Copulas for MATLAB and Octave: The HACopula Toolbox

Cited by 10 publications

References 16 publications

MATVines: A vine copula package for MATLAB

MATVines: A vine copula package for MATLAB

Outer power transformations of hierarchical Archimedean copulas: Construction, sampling and estimation

Archimedean Copulas

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