Buriticá, Gloria Naveau, Philippe

Heavy rainfall distributional modeling is essential in any impact studies linked to the water cycle, e.g.\ flood risks. Still, statistical analyses that both take into account the temporal and multivariate nature of extreme rainfall are rare, and often, a complex de-clustering step is needed to make extreme rainfall temporally independent. A natura...

Buriticá, Gloria Naveau, Philippe

First, we complement the case study of heavy rainfall in France by implementing Pareto-based methods using declustering techniques. Second, we develop on the asymptotic theory of the stable sums method. To prove Theorem 6.1, we give a more general statement and prove the multivariate central limit theory of regularly varying time series with unit (...

Bücher, Axel Posch, Peter N. Schmidtke, Philipp

We introduce a set of new Value-at-Risk independence backtests by establishing a connection between the independence property of Value-at-Risk forecasts and the extremal index, a general measure of extremal clustering of stationary sequences. We introduce a sequence of relative excess returns whose extremal index has to be estimated. We compare our...

Berghaus, Betina Bücher, Axel

The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for the extremal index are analyzed in detail. In contrast to many competitors, the estimators only depend on the ...

Chenavier, Nicolas

Let $\mathfrak{m}$ be a random tessellation in $\RR^d$ observed in a bounded Borel subset $W$ and $f(\cdot)$ be a measurable function defined on the set of convex bodies. To each cell $C$ of $\mathfrak{m}$ we associate a point $z(C)$ which is the nucleus of $C$. Applying $f(\cdot)$ to all the cells of $\mathfrak{m}$, we investigate the order statis...

Faranda, Davide Freitas, Jorge Milhazes Guiraud, Pierre Vaienti, Sandro

We present a mostly numerical investigation on randomly perturbed piecewise contracting maps (PCM) with the goal to study the extreme value limit distribution of observables related to local recurrence. Our analysis will focus on PCM under additive noise, but we will also consider the hyperbolic attractor of the Baker's map when perturbed with anot...

Avrachenkov, Konstantin Markovich, Natalia M. Sreedharan, Jithin K.

We explore the dependence structure in the sampled sequence of complex networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like node degrees, number of followers or income of the nodes in Online Social Networks etc, which satisfy two mixin...

Avrachenkov, Konstantin Markovich, Natalia M. Sreedharan, Jithin K.

We explore the dependence structure in the sampled sequence of large networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like node degrees, number of followers or income of the nodes in Online Social Networks etc, which satisfy two mixing ...

Echaust, Krzysztof
Published in
Folia Oeconomica Stetinensia

Most investors believe that left tails of the stock returns distribution are heavier than the right ones. It is a natural consequence of crashes perception as much more turbulent than the booms. Crashes develop in shorter time intervals than booms and changes of prices are significantly bigger. This paper focuses on the extreme behavior of stock ma...

Bertail, Patrice Clemencon, Stephan Tressou-Cosmao, Jessica

A theoretically sound bootstrap procedure is proposed for building accurate confidence intervals of parameters describing the extremal behavior of instantaneous functionals {f(X-n)}(n is an element of N) of a Harris Markov chain X, namely the extremal and tail indexes. Regenerative properties of the chain X (or of a Nummelin extension of the latter...