Estimating the tail-dependence coefficient: Properties and pitfalls

Frahm, Gabriel; Junker, Markus; Schmidt, Ricarda

doi:10.1016/j.insmatheco.2005.05.008

Cited by 255 publications

(253 citation statements)

References 45 publications

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“…Poulin et al (2007) made an ad hoc Monte Carlo experiment to choose the most appropriate estimator for a specific case study, retaining the Coles-Heffernan-Tawn k CHT U estimator (Coles et al 1999) and Capéraà-Fougères-Genest k CFG U estimator (Capéraà et al 1997). Poulin et al (2007) also stressed the caveats previously reported by Schmidt (2003) and Frahm et al (2005). Serinaldi (2008) exploited the relationship between k U and Kendall correlation coefficient s K to build a diagnostic plot useful for the model selection.…”

Section: Introductionmentioning

confidence: 97%

“…k U is an index that quantifies the limit probability that a variable X 1 exceeds a given t quantile x 1 given that another variable X 2 exceeds its t quantile x 2 as t ! 1 À : More formally, given the conditional probability P½F X 1 ðx 1 Þ [ tjF X 2 ðx 2 Þ [ t and introducing the copula formalism F X 1 X 2 ðx 1 ; x 2 Þ ¼ CðF X 1 ðx 1 Þ; F X 2 ðx 2 ÞÞ ¼ Cðu 1 ; u 2 Þ, where F X i , i ¼ 1; 2, denotes the univariate marginal distribution of the generic variable x i and U i :¼ F X i , k U is defined as (e.g., Frahm et al 2005) k U :¼ lim…”

Section: Introductionmentioning

confidence: 99%

“…The use of k U in hydrological analyses can be dated back to the works of Poulin et al (2007) and Serinaldi (2008) concerning bivariate frequency analyses of the annual maximum flows and the corresponding flow hydrograph volumes, and the pairwise analysis of rainfall data at multiple locations, respectively. As for the introduction of copulas in hydrology, the theoretical apparatus used in those works was essentially borrowed from econometric literature, namely, Schmidt (2003), Frahm et al (2005) and Schmidt and Stadtmüller (2006). These works provide quite extensive simulation studies devised to assess the reliability of a set of parametric and nonparametric k U estimators as well as several conclusive warnings about their use in practical analyses.…”

Section: Introductionmentioning

confidence: 99%

“…1 in Serinaldi 2008). However, Serinaldi (2008) did not perform an extensive assessment and reported only partially the caveats stated by Schmidt (2003) and Frahm et al (2005). Unfortunately, the subsequent hydrological literature relied on the first papers dealing with k U in the same field, progressively overlooking the original theoretical works.…”

Section: Introductionmentioning

confidence: 99%

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Upper tail dependence in rainfall extremes: would we know it if we saw it?

Serinaldi

Bàrdossy

Kilsby

2014

Stoch Environ Res Risk Assess

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The simultaneous occurrence of extreme events, such as simultaneous storms and floods at different locations, has a serious impact on risk assessment and mitigation strategies. The joint occurrence of extreme events can be measured by the so-called upper tail dependence (UTD) coefficient k U . In this study, we reconsider the properties of the most popular k U estimators and show that their strong bias and uncertainty make most of the empirical results reported in the hydrological literature questionable. In order to overcome the limits of k U analysis, we test several alternative tools such as a pool of formal statistical tests devised for recognizing upper tail independence and graphical diagnostics based on binary correlation and binary entropy. The reliability of all the methods is preliminarily checked by Monte Carlo experiments. Statistical tests and graphical diagnostics are therefore applied to three different rainfall data sets that allow us to explore the properties of the spatial dependence structure of rainfall extremes over a wide range of spatio-temporal scales ranging from 30 min and 1 km to 30 days and %3000 km. Results highlight that (1) classical estimators provide non zero tail dependence even for cases where it should be zero; (2) formal tests and binary correlation highlight that the pairwise spatial dependence structure can be weaker than Gaussian, thus excluding UTD calculated in a pairwise manner; (3) the binary entropy computed on triples of locations shows that the pairwise UTD is not enough to explain the spatial dependence structure of extreme rainfall, whose complexity becomes evident only after resorting to higher order correlation measures. The results concerning the bias and uncertainty of k U estimators are fully general and suggest avoiding their use especially for the short time series usually available in hydrology.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Upper tail dependence in rainfall extremes: would we know it if we saw it?

Serinaldi

Bàrdossy

Kilsby

2014

Stoch Environ Res Risk Assess

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“…The limiting values lim u↓0 λ LL (u) and lim u↓0 λ UU (u) are often called, respectively, the lower and the upper tail-dependence coefficients, and their estimation methods and applications to financial markets have been intensively studied. For details, see, for example, Caillault and Guégan [5], Frahm et al [10], Malevergne and Sornette [18], and Poon et al [21]. Remark 4.2.…”

Section: Extreme Value Dependencementioning

confidence: 99%

A multivariate Lévy process model with linear correlation

Kawai

2009

Quantitative Finance

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In this paper, we develop a multivariate risk-neutral Lévy process model and discuss its applicability in the context of the volatility smile of multiple assets. Our formulation is based upon a linear combination of independent univariate Lévy processes and can easily be calibrated to a set of one-dimensional marginal distributions and a given linear correlation matrix. We derive conditions for our formulation and the associated calibration procedure to be well defined and provide some examples associated with particular Lévy processes permitting closed form characteristic function. Numerical results of the option premiums on three currencies are presented to illustrate the effectiveness of our formulation with different linear correlation structures.

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How well do regional climate models simulate the spatial dependence of precipitation? An application of pair‐copula constructions

2015

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We investigate how well a suite of regional climate models (RCMs) from the ENSEMBLES project represents the residual spatial dependence of daily precipitation. The study area we consider is a 200 km × 200 km region in south central Norway, with RCMs driven by ERA‐40 boundary conditions at a horizontal resolution of approximately 25 km × 25 km. We model the residual spatial dependence with pair‐copula constructions, which allows us to assess both the overall and tail dependence in precipitation, including uncertainty estimates. The selected RCMs reproduce the overall dependence rather well, though the discrepancies compared to observations are substantial. All models overestimate the overall dependence in the west‐east direction. They also overestimate the upper tail dependence in the north‐south direction during winter, and in the west‐east direction during summer, whereas they tend to underestimate this dependence in the north‐south direction in summer. Moreover, many of the climate models do not simulate the small‐scale dependence patterns caused by the pronounced orography well. However, the misrepresented residual spatial dependence does not seem to affect estimates of high quantiles of extreme precipitation aggregated over a few grid boxes. The underestimation of the area‐aggregated extreme precipitation is due mainly to the well‐known underestimation of the univariate margins for individual grid boxes, suggesting that the correction of RCM biases in precipitation might be feasible.

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Estimating the tail-dependence coefficient: Properties and pitfalls

Cited by 255 publications

References 45 publications

Upper tail dependence in rainfall extremes: would we know it if we saw it?

Upper tail dependence in rainfall extremes: would we know it if we saw it?

A multivariate Lévy process model with linear correlation

How well do regional climate models simulate the spatial dependence of precipitation? An application of pair‐copula constructions

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