A flexible and tractable class of one-factor copulas

Mazo, Gildas; Girard, Sabine; Forbes, Florence

doi:10.1007/s11222-015-9580-7

Cited by 20 publications

(13 citation statements)

References 33 publications

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“…This copula has a singular component

u_{1}^{1 - θ_{1}} = ⋯ = u_{d}^{1 - θ_{d}}

and parsimonious dependence structure with d parameters θ 1 ,…, θ d . Similar copulas are studied in Mazo, Girard, and Forbes (); see also Cherubini, Durante, and Mulinacci () for the general construction principle for copulas of this type. This copula can be used in reliability theory when all of the components in a system can be simultaneously affected by a single shock.…”

Section: One‐factor Copula Model With a Linear Structurementioning

confidence: 76%

Linear factor copula models and their properties

Krupskii

Genton

2018

Scandinavian J Statistics

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We consider a special case of factor copula models with additive common factors and independent components.These models are flexible and parsimonious with O(d) parameters where d is the dimension. The linear structure allows one to obtain closed form expressions for some copulas and their extreme-value limits. These copulas can be used to model data with strong tail dependencies, such as extreme data. We study the dependence properties of these linear factor copula models and derive the corresponding limiting extreme-value copulas with a factor structure. We show how parameter estimates can be obtained for these copulas and apply one of these copulas to analyse a financial data set. ), in which the dependence structure is selected based on the likelihood, the models with a factor structure can be nicely interpreted. One example is a credit portfolio when some severe economic shocks can affect all the portfolio components, leading to multiple defaults. These shocks usually cannot be easily measured, and there might be many different factors contributing to these shocks, so it is natural to assume that these are unobserved variables.In this paper, we study the special class of factor copula models with linear structures, as proposed by Krupskii & Joe (2013). These copulas can handle a wide range of dependencies and have O(d) parameters. To construct a linear factor copula, we use a linear combination of common factors and independent factors, each having the same distribution. Similar ideas were used in the construction of generalized Archimedean copulas (Rogge & Schönbucher, 2003) and models based on comonotonic factors (Hua & Joe, 2017). Linear factor copula models are a special case of the latter models with linear loadings. The limiting extreme-value copulas (Gudendorf & Segers, 2010) with factor structures can be derived for this class of models, in closed form in some cases, and the parameters can be efficiently estimated using a composite maximum likelihood approach (for continuous copulas) or the method of moments (for copulas with singular components).The rest of the paper is organized as follows. In Section 2, we introduce the class of one-factor copula models with linear structures and study their dependence properties. We derive the limiting extreme-value copulas for this class of models and further extend this approach to models with p ≥ 2 factors in Section 3. As a special case of this class of linear factor copula models, we introduce an extension of the Marshall-Olkin copula (Marshall & Olkin, 1967) with p ≥ 2 factors affecting all of the components in a system. In Section 4, we show how the copula parameter estimates can be obtained for the models introduced in the two previous sections. In Section 5, we apply one of the proposed linear factor copula models to a financial data set, and Section 6 concludes with a discussion.

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“…This copula has a singular component

u_{1}^{1 - θ_{1}} = ⋯ = u_{d}^{1 - θ_{d}}

Section: One‐factor Copula Model With a Linear Structurementioning

confidence: 76%

Linear factor copula models and their properties

Krupskii

Genton

2018

Scandinavian J Statistics

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“…are so-called pseudo-observations. The higher dimensional structures of HAC, vine and factor copulas were estimated as described in [22], [6] and [15], respectively.…”

Section: Methodsmentioning

confidence: 99%

“…, θ > 0, and Durantesinus f (t) = sin(θt sin(θ) with parameter θ ∈ (0, π/2], please refer to [15] for �iner details. The downside of this class is a singular component present in the model, which is not natural for most economic, hydrologic or other frequently analyzed phenomenons.…”

Section: Factor Copulasmentioning

confidence: 99%

State-of-the-art in Modeling Nonlinear Dependence Among Many Random Variables with Copulas and Application to Financial Indexes

Bacigál

Komorníková

Komorník

2019

JAMRIS

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In this paper, we focus our attention on multidimensional copula models for returns of the indexes of selected prominent international financial markets. Our modeling results, based on elliptic copulas, 7dimensional hierarchical Archimedean copulas, vine copulas and factor copulas demonstrate a dominant role of the SPX index among the considered major stock indexes (mainly at the first tree of the optimal vine copulas). Some interesting weaker conditional dependencies can be detected at it's highest trees. Interestingly, while global optimal model (for the whole period of 277 months) belong to the Factor FDG copulas class, the optimal local models can be found (with very minor differences in the values of GoF test statistic) in the classes of Factor FDG and hierarchical Archimedean copulas. The dominance of these models is most striking over the interval of the financial market crisis, where the quality of the best Student class model was providing a substantially poorer fit.

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“…, d, were chosen to be regularly spaced between 0.3 and 0.9. Three situations were studied: In situation (S1), Assumption (A3) is verified, see [28]. For each situation (Si) above, the zero-step and one-step WLS estimators of Section 2.1 were tested (recall that the one-step estimator is optimal, see Proposition 1).…”

Section: Estimating the Parameters Of Multivariate Copulas Possessingmentioning

confidence: 99%

Weighted least-squares inference for multivariate copulas based on dependence coefficients

2015

Self Cite

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In this paper, we address the issue of estimating the parameters of general multivariate copulas, that is, copulas whose partial derivatives may not exist. To this aim, we consider a weighted least-squares estimator based on dependence coefficients, and establish its consistency and asymptotic normality. The estimator's performance on finite samples is illustrated on simulations and a real dataset.

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A flexible and tractable class of one-factor copulas

Cited by 20 publications

References 33 publications

Linear factor copula models and their properties

Linear factor copula models and their properties

State-of-the-art in Modeling Nonlinear Dependence Among Many Random Variables with Copulas and Application to Financial Indexes

Weighted least-squares inference for multivariate copulas based on dependence coefficients

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