A New Class of Models for Bivariate Joint Tails

Ramos, Alexandra; Ledford, Anthony

doi:10.1111/j.1467-9868.2008.00684.x

Cited by 68 publications

(78 citation statements)

References 36 publications

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“…There also exists a large statistics literature to assess the extremal behavior of multivariate vectors or time series; see e.g. Ledford and Tawn (2003) and Ramos and Ledford (2008) and references therein.…”

Section: Introductionmentioning

confidence: 99%

High-level dependence in time series models

2009

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We present several notions of high-level dependence for stochastic processes, which have appeared in the literature. We calculate such measures for discrete and continuous-time models, where we concentrate on time series with heavy-tailed marginals, where extremes are likely to occur in clusters. Such models include linear models and solutions to random recurrence equations; in particular, discrete and continuous-time moving average and (G)ARCH processes. To illustrate our results we present a small simulation study.

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Section: Introductionmentioning

confidence: 99%

High-level dependence in time series models

2009

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“…Ramos and Ledford, 2009;Cooley et al, 2010]. We recall that the unit Frechet distribution P X x ð Þ¼exp À1=x ð Þ for x > 0 is maxstable.…”

Section: Defining Extreme Precipitation Deficitsmentioning

confidence: 99%

“…where L represents a bivariate slowly varying function [Ramos and Ledford, 2009;Resnick, 2007]. A fundamental feature of equation (5) is the so-called tail dependence coefficient 2 0; 1 ð that encapsulates the strength of asymptotic independence.…”

Section: The Fragility Index Fi Inferencementioning

confidence: 99%

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Spatial assessment of precipitation deficits in the Duero basin (central Spain) with multivariate extreme value statistics

2013

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[1] Nonirrigated agriculture on the Iberian Peninsula is regularly affected by dry periods that can cause important losses. This paper focuses on the comparison of the classical Standard Precipitation Index (SPI) with a fragility index developed by the multivariate extreme value theory community, which is used to describe monthly precipitation deficits below 30.5 mm (about 1 mm/d) in the Spanish Duero basin. The multivariate extreme value model allows to capture relevant information concerning the dependence structure among extreme precipitation deficits. Maps of those extremal dependence summaries and of loadings of principal components of the SPI provide quantitative information for water management. In addition, jointly analyzing data from several stations improves the inference of uncertainty. Spatial patterns of extremal dependence emerged with respect to orographic features. Most severe dry spells occur in the southeast of the Duero basin. In central plain of the Duero basin, a predominantly agricultural area, a strong fragility index for severity of dry spells is particularly found in eastern regions. Results of the MEVT and SPI analysis point in the same direction. Beyond this, the MEVT assessment gives a quantitative measure of the dependence between stations and regions. Estimates of return periods for extreme dry spell severity are discussed. Deficits below 42.7 mm are also analyzed.Citation: Kallache, M., P. Naveau, and M. Vrac (2013), Spatial assessment of precipitation deficits in the Duero basin (central Spain) with multivariate extreme value statistics, Water Resour. Res., 49,[6716][6717][6718][6719][6720][6721][6722][6723][6724][6725][6726][6727][6728][6729][6730]

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“…Further, bivariate tail dependence decay as h ! 1 for time series data is rarely modeled by bivariate power-law decay Tawn 2003, Ramos andLedford 2009) or theory is ignored (Ledford and Tawn 2003), or decay is ignored (St¼ aric¼ a (1999).…”

Section: Tail Event Correlation and Extremogrammentioning

confidence: 99%

Tail and Nontail Memory With Applications to Extreme Value and Robust Statistics

Hill¹

2011

Econom. Theory

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New notions of tail and non-tail dependence are used to characterize separately extremal and non-extremal information, including tail log-exceedances and events, and tail-trimmed levels. We prove Near Epoch Dependence (McLeish 1975, Gallant andWhite 1988) and L 0 -Approximability (Pötscher and Prucha 1991) are equivalent for tail events and tail-trimmed levels, ensuring a Gaussian central limit theory for important extreme value and robust statistics under general conditions. We apply the theory to characterize the extremal and nonextremal memory properties of possibly very heavy tailed GARCH processes and distributed lags. This in turn is used to verify Gaussian limits for tail index, tail dependence and tail trimmed sums of these data, allowing for Gaussian asymptotics for a new Tail-Trimmed Least Squares estimator for heavy tailed processes.

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A New Class of Models for Bivariate Joint Tails

Cited by 68 publications

References 36 publications

High-level dependence in time series models

High-level dependence in time series models

Spatial assessment of precipitation deficits in the Duero basin (central Spain) with multivariate extreme value statistics

Tail and Nontail Memory With Applications to Extreme Value and Robust Statistics

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