scholarly journals An Analysis of a Heuristic Procedure to Evaluate Tail (in)dependence

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Marta Ferreira ◽  
Sérgio Silva
Keyword(s):  
Applied Sciences ◽  
Extreme Events ◽  
Tail Dependence ◽  
Extreme Value ◽  
Asymptotic Independence ◽  
Heuristic Procedure ◽  
Asymptotic Dependence ◽  
Simulation Based ◽  
Tail Dependence Coefficient

Measuring tail dependence is an important issue in many applied sciences in order to quantify the risk of simultaneous extreme events. A usual measure is given by the tail dependence coefficient. The characteristics of events behave quite differently as these become more extreme, whereas we are in the class of asymptotic dependence or in the class of asymptotic independence. The literature has emphasized the asymptotic dependent class but wrongly infers that tail dependence will result in the overestimation of extreme value dependence and consequently of the risk. In this paper we analyze this issue through simulation based on a heuristic procedure.

scholarly journals SYSTEMIC RISK: AN ASYMPTOTIC EVALUATION

2017 ◽  
Vol 48 (02) ◽  
pp. 673-698 ◽  
Author(s):  
Alexandru V. Asimit ◽  
Jinzhu Li
Keyword(s):  
Systemic Risk ◽  
Financial Distress ◽  
Mathematical Formulation ◽  
Tail Dependence ◽  
Value Theory ◽  
Asymptotic Independence ◽  
Regulatory Capital ◽  
Asymptotic Dependence ◽  
Asymptotic Evaluation ◽  
Mathematical Definitions

AbstractSystemic risk (SR) has been shown to play an important role in explaining the financial turmoils in the last several decades and understanding this source of risk has been a particular interest amongst academics, practitioners and regulators. The precise mathematical formulation of SR is still scrutinised, but the main purpose is to evaluate the financial distress of a system as a result of the failure of one component of the financial system in question. Many of the mathematical definitions of SR are based on evaluating expectations in extreme regions and therefore, Extreme Value Theory (EVT) represents the key ingredient in producing valuable estimates of SR and even its decomposition per individual components of the entire system. Without doubt, the prescribed dependence model amongst the system components has a major impact over our asymptotic approximations. Thus, this paper considers various well-known dependence models in the EVT literature that allow us to generate SR estimates. Our findings reveal that SR has a significant impact under asymptotic dependence, while weak tail dependence, known as asymptotic independence, produces an insignificant loss over the regulatory capital.

scholarly journals Hoeffding–Sobol decomposition of homogeneous co-survival functions: from Choquet representation to extreme value theory application

2021 ◽  
Vol 9 (1) ◽  
pp. 179-198
Author(s):  
Cécile Mercadier ◽  
Paul Ressel
Keyword(s):  
Random Vector ◽  
Extreme Value Theory ◽  
Tail Dependence ◽  
Value Theory ◽  
Extreme Value ◽  
Survival Functions ◽  
Main Ingredient ◽  
Asymptotic Dependence ◽  
Dependence Function ◽  
Theory Application

Abstract The paper investigates the Hoeffding–Sobol decomposition of homogeneous co-survival functions. For this class, the Choquet representation is transferred to the terms of the functional decomposition, and in addition to their individual variances, or to the superset combinations of those. The domain of integration in the resulting formulae is reduced in comparison with the already known expressions. When the function under study is the stable tail dependence function of a random vector, ranking these superset indices corresponds to clustering the components of the random vector with respect to their asymptotic dependence. Their Choquet representation is the main ingredient in deriving a sharp upper bound for the quantities involved in the tail dependograph, a graph in extreme value theory that summarizes asymptotic dependence.

scholarly journals On Conditional Value at Risk (CoVaR) for tail-dependent copulas

2017 ◽  
Vol 5 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Piotr Jaworski
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Tail Dependence ◽  
Extreme Value ◽  
Conditional Value At Risk ◽  
Dependence Function ◽  
Conditioning Event

Abstract The paper deals with Conditional Value at Risk (CoVaR) for copulas with nontrivial tail dependence. We show that both in the standard and the modified settings, the tail dependence function determines the limiting properties of CoVaR as the conditioning event becomes more extreme. The results are illustrated with examples using the extreme value, conic and truncation invariant families of bivariate tail-dependent copulas.

scholarly journals Multivariate Extreme Value Theory - A Tutorial with Applications to Hydrology and Meteorology

2014 ◽  
Vol 2 (1) ◽  
Author(s):  
Anne Dutfoy ◽  
Sylvie Parey ◽  
Nicolas Roche
Keyword(s):  
Extreme Value Theory ◽  
High Speed ◽  
Value Theory ◽  
Extreme Value ◽  
Asymptotic Independence ◽  
Data Sets ◽  
Overhead Lines ◽  
Multivariate Extreme Value Theory ◽  
Air Temperatures ◽  
Multivariate Extreme Value

AbstractIn this paper, we provide a tutorial on multivariate extreme value methods which allows to estimate the risk associated with rare events occurring jointly. We draw particular attention to issues related to extremal dependence and we insist on the asymptotic independence feature. We apply the multivariate extreme value theory on two data sets related to hydrology and meteorology: first, the joint flooding of two rivers, which puts at risk the facilities lying downstream the confluence; then the joint occurrence of high speed wind and low air temperatures, which might affect overhead lines.

scholarly journals Extreme events in total ozone over Arosa – Part 1: Application of extreme value theory

2010 ◽  
Vol 10 (20) ◽  
pp. 10021-10031 ◽  
Author(s):  
H. E. Rieder ◽  
J. Staehelin ◽  
J. A. Maeder ◽  
T. Peter ◽  
M. Ribatet ◽  
...  
Keyword(s):  
Time Series ◽  
Frequency Distribution ◽  
Extreme Events ◽  
Extreme Value Theory ◽  
Total Ozone ◽  
Volcanic Eruptions ◽  
Value Theory ◽  
Extreme Value ◽  
Data Set ◽  
Ozone Data

Abstract. In this study ideas from extreme value theory are for the first time applied in the field of stratospheric ozone research, because statistical analysis showed that previously used concepts assuming a Gaussian distribution (e.g. fixed deviations from mean values) of total ozone data do not adequately address the structure of the extremes. We show that statistical extreme value methods are appropriate to identify ozone extremes and to describe the tails of the Arosa (Switzerland) total ozone time series. In order to accommodate the seasonal cycle in total ozone, a daily moving threshold was determined and used, with tools from extreme value theory, to analyse the frequency of days with extreme low (termed ELOs) and high (termed EHOs) total ozone at Arosa. The analysis shows that the Generalized Pareto Distribution (GPD) provides an appropriate model for the frequency distribution of total ozone above or below a mathematically well-defined threshold, thus providing a statistical description of ELOs and EHOs. The results show an increase in ELOs and a decrease in EHOs during the last decades. The fitted model represents the tails of the total ozone data set with high accuracy over the entire range (including absolute monthly minima and maxima), and enables a precise computation of the frequency distribution of ozone mini-holes (using constant thresholds). Analyzing the tails instead of a small fraction of days below constant thresholds provides deeper insight into the time series properties. Fingerprints of dynamical (e.g. ENSO, NAO) and chemical features (e.g. strong polar vortex ozone loss), and major volcanic eruptions, can be identified in the observed frequency of extreme events throughout the time series. Overall the new approach to analysis of extremes provides more information on time series properties and variability than previous approaches that use only monthly averages and/or mini-holes and mini-highs.

TAIL AND NONTAIL MEMORY WITH APPLICATIONS TO EXTREME VALUE AND ROBUST STATISTICS

2011 ◽  
Vol 27 (4) ◽  
pp. 844-884 ◽  
Author(s):  
Jonathan B. Hill
Keyword(s):  
Least Squares ◽  
Central Limit ◽  
Robust Statistics ◽  
Tail Dependence ◽  
Extreme Value ◽  
Limit Theory ◽  
Trimmed Sums ◽  
Garch Processes ◽  
Heavy Tailed ◽  
Tail Events

New notions of tail and nontail dependence are used to characterize separately extremal and nonextremal information, including tail log-exceedances and events, and tail-trimmed levels. We prove that near epoch dependence (McLeish, 1975; Gallant and White, 1988) and L0-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.

scholarly journals Extreme weather exposure identification for road networks – a comparative assessment of statistical methods

2017 ◽  
Vol 17 (4) ◽  
pp. 515-531 ◽  
Author(s):  
Matthias Schlögl ◽  
Gregor Laaha
Keyword(s):  
Extreme Events ◽  
Information Gain ◽  
Extreme Weather ◽  
Extreme Value ◽  
Added Value ◽  
Extreme Value Statistics ◽  
Extreme Weather Events ◽  
Mean Residual Life ◽  
Data Set ◽  
Return Levels

Abstract. The assessment of road infrastructure exposure to extreme weather events is of major importance for scientists and practitioners alike. In this study, we compare the different extreme value approaches and fitting methods with respect to their value for assessing the exposure of transport networks to extreme precipitation and temperature impacts. Based on an Austrian data set from 25 meteorological stations representing diverse meteorological conditions, we assess the added value of partial duration series (PDS) over the standardly used annual maxima series (AMS) in order to give recommendations for performing extreme value statistics of meteorological hazards. Results show the merits of the robust L-moment estimation, which yielded better results than maximum likelihood estimation in 62 % of all cases. At the same time, results question the general assumption of the threshold excess approach (employing PDS) being superior to the block maxima approach (employing AMS) due to information gain. For low return periods (non-extreme events) the PDS approach tends to overestimate return levels as compared to the AMS approach, whereas an opposite behavior was found for high return levels (extreme events). In extreme cases, an inappropriate threshold was shown to lead to considerable biases that may outperform the possible gain of information from including additional extreme events by far. This effect was visible from neither the square-root criterion nor standardly used graphical diagnosis (mean residual life plot) but rather from a direct comparison of AMS and PDS in combined quantile plots. We therefore recommend performing AMS and PDS approaches simultaneously in order to select the best-suited approach. This will make the analyses more robust, not only in cases where threshold selection and dependency introduces biases to the PDS approach but also in cases where the AMS contains non-extreme events that may introduce similar biases. For assessing the performance of extreme events we recommend the use of conditional performance measures that focus on rare events only in addition to standardly used unconditional indicators. The findings of the study directly address road and traffic management but can be transferred to a range of other environmental variables including meteorological and hydrological quantities.

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