scholarly journals Determining the dependence structure of multivariate extremes

Biometrika ◽  
2020 ◽  
Vol 107 (3) ◽  
pp. 513-532
Author(s):  
E S Simpson ◽  
J L Wadsworth ◽  
J A Tawn
Keyword(s):  
Statistical Models ◽  
Regular Variation ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Dependence Structure ◽  
Value Analysis ◽  
Extremal Dependence ◽  
Measures Of Dependence ◽  
Hidden Regular Variation ◽  
Multivariate Extreme Value

Summary In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies in determining which subsets of variables can take their largest values simultaneously while the others are of smaller order. Our approach to this problem exploits hidden regular variation properties on a collection of nonstandard cones, and provides a new set of indices that reveal aspects of the extremal dependence structure not available through existing measures of dependence. We derive theoretical properties of these indices, demonstrate their utility through a series of examples, and develop methods of inference that also estimate the proportion of extremal mass associated with each cone. We apply the methods to river flows in the U.K., estimating the probabilities of different subsets of sites being large simultaneously.

scholarly journals Deriving the 100-Year Total Water Level around the Coast of Corsica by Combining Trivariate Extreme Value Analysis and Coastal Hydrodynamic Models

2021 ◽  
Vol 9 (12) ◽  
pp. 1347
Author(s):  
Jessie Louisor ◽  
Jérémy Rohmer ◽  
Thomas Bulteau ◽  
Faïza Boulahya ◽  
Rodrigo Pedreros ◽  
...  
Keyword(s):  
Water Level ◽  
Return Period ◽  
Extreme Value ◽  
Coastal Areas ◽  
Extreme Value Analysis ◽  
Total Water ◽  
Hydrodynamic Models ◽  
Value Analysis ◽  
Multivariate Extreme Value ◽  
Total Water Level

As low-lying coastal areas can be impacted by flooding caused by dynamic components that are dependent on each other (wind, waves, water levels—tide, atmospheric surge, currents), the analysis of the return period of a single component is not representative of the return period of the total water level at the coast. It is important to assess a joint return period of all the components. Based on a semiparametric multivariate extreme value analysis, we determined the joint probabilities that significant wave heights (Hs), wind intensity at 10 m above the ground (U), and still water level (SWL) exceeded jointly imposed thresholds all along the Corsica Island coasts (Mediterranean Sea). We also considered the covariate peak direction (Dp), the peak period (Tp), and the wind direction (Du). Here, we focus on providing extreme scenarios to populate coastal hydrodynamic models, SWAN and SWASH-2DH, in order to compute the 100-year total water level (100y-TWL) all along the coasts. We show how the proposed multivariate extreme value analysis can help to more accurately define low-lying zones potentially exposed to coastal flooding, especially in Corsica where a unique value of 2 m was taken into account in previous studies. The computed 100y-TWL values are between 1 m along the eastern coasts and a maximum of 1.8 m on the western coast. The calculated values are also below the 2.4 m threshold recommended when considering the sea level rise (SLR). This highlights the added value of performing a full integration of extreme offshore conditions, together with their dependence on hydrodynamic simulations for screening out the coastal areas potentially exposed to flooding.

scholarly journals Bitcoin and Cryptocurrencies—Not for the Faint-Hearted

2017 ◽  
Vol 4 (1) ◽  
pp. 56 ◽  
Author(s):  
Joerg Osterrieder ◽  
Martin Strika ◽  
Julian Lorenz
Keyword(s):  
Financial Engineering ◽  
Heavy Tails ◽  
Tail Dependence ◽  
Extreme Value ◽  
Point Of View ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Risk Characteristics ◽  
Asset Class ◽  
Multivariate Extreme Value

Cryptocurrencies became popular with the emergence of Bitcoin and have shown an unprecedented growth over the last few years. As of November 2016, more than 720 cryptocurrencies exist, with Bitcoin still being the most popular one. We provide both a statistical analysis as well as an extreme value analysis of the returns of the most important cryptocurrencies. A particular focus is on the tail risk characteristics and we will provide an in-depth univariate and multivariate extreme value analysis. The tail dependence of cryptocurrencies is investigated (using both empirical and Gaussian copulas). For investors—especially institutional ones—as well as regulators, an understanding of the risk and tail characteristics are of utmost importance. For cryptocurrencies to become a mainstream investable asset class, studying these properties is necessary. Our findings show that cryptocurrencies exhibit strong non-normal characteristics, large tail dependencies, depending on the particular cryptocurrencies and heavy tails. Statistical similarities can be observed for cryptocurrencies that share the same underlying technology. This has implications for risk management, financial engineering (such as derivatives on cryptocurrencies)—both from an investor’s as well as from a regulator’s point of view. To our knowledge, this is the first detailed study looking at the extreme value behaviour of cryptocurrencies, their correlations and tail dependencies as well as their statistical properties.

Relations Between Hidden Regular Variation and the Tail Order of Copulas

2014 ◽  
Vol 51 (01) ◽  
pp. 37-57 ◽  
Author(s):  
Lei Hua ◽  
Harry Joe ◽  
Haijun Li
Keyword(s):  
Integral Representation ◽  
Random Vector ◽  
Regular Variation ◽  
Dependence Structure ◽  
Multivariate Regular Variation ◽  
Intensity Measures ◽  
Extremal Dependence ◽  
Measure Representation ◽  
Hidden Regular Variation ◽  
Type Integral

We study the relations between the tail order of copulas and hidden regular variation (HRV) on subcones generated by order statistics. Multivariate regular variation (MRV) and HRV deal with extremal dependence of random vectors with Pareto-like univariate margins. Alternatively, if one uses a copula to model the dependence structure of a random vector then the upper exponent and tail order functions can be used to capture the extremal dependence structure. After defining upper exponent functions on a series of subcones, we establish the relation between the tail order of a copula and the tail indexes for MRV and HRV. We show that upper exponent functions of a copula and intensity measures of MRV/HRV can be represented by each other, and the upper exponent function on subcones can be expressed by a Pickands-type integral representation. Finally, a mixture model is given with the mixing random vector leading to the finite-directional measure in a product-measure representation of HRV intensity measures.

scholarly journals Relations Between Hidden Regular Variation and the Tail Order of Copulas

2014 ◽  
Vol 51 (1) ◽  
pp. 37-57 ◽  
Author(s):  
Lei Hua ◽  
Harry Joe ◽  
Haijun Li
Keyword(s):  
Integral Representation ◽  
Random Vector ◽  
Regular Variation ◽  
Dependence Structure ◽  
Multivariate Regular Variation ◽  
Intensity Measures ◽  
Extremal Dependence ◽  
Measure Representation ◽  
Hidden Regular Variation ◽  
Type Integral

We study the relations between the tail order of copulas and hidden regular variation (HRV) on subcones generated by order statistics. Multivariate regular variation (MRV) and HRV deal with extremal dependence of random vectors with Pareto-like univariate margins. Alternatively, if one uses a copula to model the dependence structure of a random vector then the upper exponent and tail order functions can be used to capture the extremal dependence structure. After defining upper exponent functions on a series of subcones, we establish the relation between the tail order of a copula and the tail indexes for MRV and HRV. We show that upper exponent functions of a copula and intensity measures of MRV/HRV can be represented by each other, and the upper exponent function on subcones can be expressed by a Pickands-type integral representation. Finally, a mixture model is given with the mixing random vector leading to the finite-directional measure in a product-measure representation of HRV intensity measures.

Multivariate extreme value analysis of a moored semi-submersible

1997 ◽  
Vol 10 (6) ◽  
pp. 443-463
Author(s):  
John Bowers ◽  
Ian Morton ◽  
Gill Mould
Keyword(s):  
Extreme Value ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Multivariate Extreme Value
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