Beyond simplified pair-copula constructions

Acar, Elif F.; Genest, Christian; Nešlehová, Johanna

doi:10.1016/j.jmva.2012.02.001

Cited by 121 publications

(119 citation statements)

References 12 publications

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“…On one side, [27] a rms that this simplifying assumption is not only required for fast, exible, and robust inference, but that it provides "a rather good approximation, even when the simplifying assumption is far from being ful lled by the actual model". On the other side, [4] maintains that "this view is too optimistic". The latter authors propose a visual test of H when d = and in a parametric framework.…”

Section: Remark 1 the Simplifying Assumption H Does Not Imply That Cmentioning

confidence: 99%

About tests of the “simplifying” assumption for conditional copulas

Derumigny

Fermanian

2017

Dependence Modeling

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Abstract:We discuss the so-called "simplifying assumption" of conditional copulas in a general framework. We introduce several tests of the latter assumption for non-and semiparametric copula models. Some related test procedures based on conditioning subsets instead of point-wise events are proposed. The limiting distributions of such test statistics under the null are approximated by several bootstrap schemes, most of them being new. We prove the validity of a particular semiparametric bootstrap scheme. Some simulations illustrate the relevance of our results.

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Section: Remark 1 the Simplifying Assumption H Does Not Imply That Cmentioning

confidence: 99%

About tests of the “simplifying” assumption for conditional copulas

Derumigny

Fermanian

2017

Dependence Modeling

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“…Therefore, this lack of flexibility of copulas would be a limitation for many types of compound events. Pair-copula constructions (PCCs) decompose the dependence structure into bivariate copulas (some of which are conditional) and give greater flexibility in modelling generic high-dimensional systems compared to multivariate parametric copulas (Aas et al, 2009;Acar et al, 2012;Bedford and Cooke, 2002;Hobaek Haff, 2012).…”

Section: Introductionmentioning

confidence: 99%

Multivariate statistical modelling of compound events via pair-copula constructions: analysis of floods in Ravenna (Italy)

Bevacqua

Maraun

Haff

et al. 2017

Hydrol. Earth Syst. Sci.

266

304

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Abstract. Compound events (CEs) are multivariate extreme events in which the individual contributing variables may not be extreme themselves, but their joint -dependent -occurrence causes an extreme impact. Conventional univariate statistical analysis cannot give accurate information regarding the multivariate nature of these events. We develop a conceptual model, implemented via pair-copula constructions, which allows for the quantification of the risk associated with compound events in present-day and future climate, as well as the uncertainty estimates around such risk. The model includes predictors, which could represent for instance meteorological processes that provide insight into both the involved physical mechanisms and the temporal variability of compound events. Moreover, this model enables multivariate statistical downscaling of compound events. Downscaling is required to extend the compound events' risk assessment to the past or future climate, where climate models either do not simulate realistic values of the local variables driving the events or do not simulate them at all. Based on the developed model, we study compound floods, i.e. joint storm surge and high river runoff, in Ravenna (Italy). To explicitly quantify the risk, we define the impact of compound floods as a function of sea and river levels. We use meteorological predictors to extend the analysis to the past, and get a more robust risk analysis. We quantify the uncertainties of the risk analysis, observing that they are very large due to the shortness of the available data, though this may also be the case in other studies where they have not been estimated. Ignoring the dependence between sea and river levels would result in an underestimation of risk; in particular, the expected return period of the highest compound flood observed increases from about 20 to 32 years when switching from the dependent to the independent case.

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“…Once we selected a structure, we make the simplifying assumption that copulas of conditional distributions do not directly depend on the conditioning variable in order to keep inference and model selection fast and robust. While Haff et al (2010) showed that a simplified pair copula decomposition can be a good approximation even when the assumption is far from being fulfilled, Acar et al (2012) illustrated that it can also be misleading. To simulate time series, we sample recursively according to well known algorithms using the inverse conditional copulas corresponding to the R-vine density decomposition in (3) (Kurowicka and Cooke 2006;Aas et al 2009).…”

Section: Definition 2 Vine R-vinementioning

confidence: 99%

A Vine-Copula Model for Time Series of Significant Wave Heights and Mean Zero-Crossing Periods in the North Sea

Jaeger

Morales-Nápoles

2017

ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.

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Stochastic description and simulation of oceanographic variables are essential for coastal and marine engineering applications. In the past decade, copula-based approaches have become increasingly popular to estimate the multivariate distribution of some variables at the peak of a storm along with its duration. The modeling of the storm shape, which contributes to its impact, is often simplified. This article proposes a vine-copula approach to characterize hourly significant wave heights and corresponding mean zero-crossing periods as a random process in time. The model is applied to a data set in the North Sea and time series with the duration of an oceanographic winter are simulated. The synthetic wave scenarios emulate storms as well as daily conditions. The results are for example useful as input for coastal risk analyses and for planning offshore operations. Nonetheless, selecting a vine structure, finding appropriate copula families and estimating parameters is not straightforward. The validity of the model, as well as the conclusions that can be drawn from it, are sensitive to these choices. A valuable by-product of the proposed vine-copula approach is the bivariate distribution of significant wave heights and corresponding mean zero-crossing periods at the given location. Its dependence structure is approximated by the flexible skew-t copula family and preserves the limiting wave steepness condition. INTRODUCTIONWind-induced sea waves affect coastlines, marine structures and offshore operations. Unfavorable conditions can cause significant morphological change, damages or downtime. Intuitively, the higher a wave, the more energy it carries and the more destructive

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Beyond simplified pair-copula constructions

Cited by 121 publications

References 12 publications

About tests of the “simplifying” assumption for conditional copulas

About tests of the “simplifying” assumption for conditional copulas

Multivariate statistical modelling of compound events via pair-copula constructions: analysis of floods in Ravenna (Italy)

A Vine-Copula Model for Time Series of Significant Wave Heights and Mean Zero-Crossing Periods in the North Sea

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