Related papers: Tail copula representation of path-based maximal t…
A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is…
Stochastic volatility processes with heavy-tailed innovations are a well-known model for financial time series. In these models, the extremes of the log returns are mainly driven by the extremes of the i.i.d. innovation sequence which leads…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
The risk of catastrophes is related to the possibility of occurring extreme values. Several statistical methodologies have been developed in order to evaluate the propensity of a process for the occurrence of high values and the permanence…
This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of…
Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case…
The extremal behaviour of a Markov chain is typically characterized by its tail chain. For asymptotically dependent Markov chains existing formulations fail to capture the full evolution of the extreme event when the chain moves out of the…
A common object to describe the extremal dependence of a $d$-variate random vector $X$ is the stable tail dependence function $L$. Various parametric models have emerged, with a popular subclass consisting of those stable tail dependence…
The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having…
In this paper, a novel approach to the problem of estimating the heavy-tail exponent alpha>0 of a distribution is proposed. It is based on the fact that block-maxima of size m of the independent and identically distributed data scale at a…
We introduce a Markov product structure for multivariate tail dependence functions, building upon the well-known Markov product for copulas. We investigate algebraic and monotonicity properties of this new product as well as its role in…
Extremal dependence describes the strength of correlation between the largest observations of two variables. It is usually measured with symmetric dependence coefficients that do not depend on the order of the variables. In many cases,…
Employing the framework of regular variation, we propose two decompositions which help to summarize and describel high-dimensional tail dependence. Via transformation, we define a vector space on the positive orthant, yielding the notion of…
Determining the causes of extreme events is a fundamental question in many scientific fields. An important aspect when modelling multivariate extremes is the tail dependence. In application, the extreme dependence structure may…
Tail dependence models for distributions attracted to a max-stable law are fitted using observations above a high threshold. To cope with spatial, high-dimensional data, a rank-based M-estimator is proposed relying on bivariate margins…
Copulas have become an important tool in the modern best practice Enterprise Risk Management, often supplanting other approaches to modelling stochastic dependence. However, choosing the `right' copula is not an easy task, and the…
This paper investigates the asymptotic behavior of higher-order conditional tail moments, which quantify the contribution of individual losses in the event of systemic collapse. The study is conducted within a framework comprising two…
Dependence strucuture estimation is one of the important problems in machine learning domain and has many applications in different scientific areas. In this paper, a theoretical framework for such estimation based on copula and copula…
Network latencies have become increasingly important for the performance of web servers and cloud computing platforms. Identifying network-related tail latencies and reasoning about their potential causes is especially important to gauge…
In this paper, we consider a simple estimator for tail dependence coefficients of a max-stable time series and show its asymptotic normality under a mild condition. The novelty of our result is that this condition does not involve mixing…