Related papers: Inference on the tail process with application to …
We investigate a family of discrete-time stationary processes defined by multiple stable integrals and renewal processes with infinite means. The model may exhibit behaviors of short-range or long-range dependence, respectively, depending…
We consider heavy-tailed distributions and compare the well-known estimators of the tail index, based on extreme value theory with a comparatively recent estimator based on a different idea.
In this paper, we develop a comprehensive asymptotic and bootstrap theory for checkerboard-based estimation of lower and upper tail copulas under unknown marginal distributions. The estimator is constructed via local bilinear (checkerboard)…
For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals…
Einmahl, de Haan and Zhou (2016, Journal of the Royal Statistical Society: Series B, 78(1), 31-51) recently introduced a stochastic model that allows for heteroscedasticity of extremes. The model is extended to the situation where the…
In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…
Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian…
By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These…
Both parametric distribution functions appearing in extreme value theory - the generalized extreme value distribution and the generalized Pareto distribution - have log-concave densities if the extreme value index gamma is in [-1,0].…
For discrete-valued time series, predictive inference cannot be implemented through the construction of prediction intervals to some predetermined coverage level, as this is the case for real-valued time series. To address this problem, we…
Conditions for geometric ergodicity of multivariate autoregressive conditional heteroskedasticity (ARCH) processes, with the so-called BEKK (Baba, Engle, Kraft, and Kroner) parametrization, are considered. We show for a class of BEKK-ARCH…
The modelling of multivariate extreme events is important in a wide variety of applications, including flood risk analysis, metocean engineering and financial modelling. A wide variety of statistical techniques have been proposed in the…
We propose a set of dependence measures that are non-linear, local, invariant to a wide range of transformations on the marginals, can show tail and risk asymmetries, are always well-defined, are easy to estimate and can be used on any…
The goal of this paper is to investigate the tools of extreme value theory originally introduced for discrete time stationary stochastic processes (time series), namely the tail process and the tail measure, in the framework of continuous…
In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…
This paper is concerned with tests for changes in the jump behaviour of a time-continuous process. Based on results on weak convergence of a sequential empirical tail integral process, asymptotics of certain tests statistics for breaks in…
There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the flexible class of max-stable vectors down to simple and concise summary measures like the…
This paper investigates pooling strategies for tail index and extreme quantile estimation from heavy-tailed data. To fully exploit the information contained in several samples, we present general weighted pooled Hill estimators of the tail…
Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov…
The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual…